Solve operatorname{RP}2/3[2-(x/3+6)-2(x-1)]=5/6x-1

$$\operatorname { RP } \frac { 2 } { 3 } [ 2 - ( \frac { x } { 3 } + 6 ) - 2 ( x - 1 ) ] = \frac { 5 } { 6 } x - 1$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=-\frac{3\left(5x-6\right)}{4R\left(7x+6\right)}\text{, }&x\neq -\frac{6}{7}\text{ and }R\neq 0\\P\in \mathrm{C}\text{, }&x=\frac{6}{5}\text{ and }R=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$6RP\times \frac{2}{3}\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

Multiply 6 and \frac{2}{3} to get 4.

$$4RP\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

To find the opposite of \frac{x}{3}+6, find the opposite of each term.

$$4RP\left(2-\frac{x}{3}-6-2\left(x-1\right)\right)=5x-6$$

Subtract 6 from 2 to get -4.

$$4RP\left(-4-\frac{x}{3}-2\left(x-1\right)\right)=5x-6$$

Use the distributive property to multiply -2 by x-1.

$$4RP\left(-4-\frac{x}{3}-2x+2\right)=5x-6$$

Add -4 and 2 to get -2.

$$4RP\left(-2-\frac{x}{3}-2x\right)=5x-6$$

Use the distributive property to multiply 4RP by -2-\frac{x}{3}-2x.

$$-8PR-4PR\times \frac{x}{3}-8PRx=5x-6$$

Express -4\times \frac{x}{3} as a single fraction.

$$-8PR+\frac{-4x}{3}PR-8PRx=5x-6$$

Express \frac{-4x}{3}P as a single fraction.

$$-8PR+\frac{-4xP}{3}R-8PRx=5x-6$$

Express \frac{-4xP}{3}R as a single fraction.

$$-8PR+\frac{-4xPR}{3}-8PRx=5x-6$$

Multiply both sides of the equation by 3.

$$-24PR-4xPR-24PRx=15x-18$$

Combine -4xPR and -24PRx to get -28xPR.

$$-24PR-28xPR=15x-18$$

Combine all terms containing P.

$$\left(-24R-28xR\right)P=15x-18$$

The equation is in standard form.

$$\left(-28Rx-24R\right)P=15x-18$$

Divide both sides by -24R-28xR.

$$\frac{\left(-28Rx-24R\right)P}{-28Rx-24R}=\frac{15x-18}{-28Rx-24R}$$

Dividing by -24R-28xR undoes the multiplication by -24R-28xR.

$$P=\frac{15x-18}{-28Rx-24R}$$

Divide 15x-18 by -24R-28xR.

$$P=-\frac{3\left(5x-6\right)}{4R\left(7x+6\right)}$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=-\frac{3\left(5x-6\right)}{4P\left(7x+6\right)}\text{, }&x\neq -\frac{6}{7}\text{ and }P\neq 0\\R\in \mathrm{C}\text{, }&x=\frac{6}{5}\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$6RP\times \frac{2}{3}\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

Multiply 6 and \frac{2}{3} to get 4.

$$4RP\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

To find the opposite of \frac{x}{3}+6, find the opposite of each term.

$$4RP\left(2-\frac{x}{3}-6-2\left(x-1\right)\right)=5x-6$$

Subtract 6 from 2 to get -4.

$$4RP\left(-4-\frac{x}{3}-2\left(x-1\right)\right)=5x-6$$

Use the distributive property to multiply -2 by x-1.

$$4RP\left(-4-\frac{x}{3}-2x+2\right)=5x-6$$

Add -4 and 2 to get -2.

$$4RP\left(-2-\frac{x}{3}-2x\right)=5x-6$$

Use the distributive property to multiply 4RP by -2-\frac{x}{3}-2x.

$$-8PR-4PR\times \frac{x}{3}-8PRx=5x-6$$

Express -4\times \frac{x}{3} as a single fraction.

$$-8PR+\frac{-4x}{3}PR-8PRx=5x-6$$

Express \frac{-4x}{3}P as a single fraction.

$$-8PR+\frac{-4xP}{3}R-8PRx=5x-6$$

Express \frac{-4xP}{3}R as a single fraction.

$$-8PR+\frac{-4xPR}{3}-8PRx=5x-6$$

Multiply both sides of the equation by 3.

$$-24PR-4xPR-24PRx=15x-18$$

Combine -4xPR and -24PRx to get -28xPR.

$$-24PR-28xPR=15x-18$$

Combine all terms containing R.

$$\left(-24P-28xP\right)R=15x-18$$

The equation is in standard form.

$$\left(-28Px-24P\right)R=15x-18$$

Divide both sides by -24P-28xP.

$$\frac{\left(-28Px-24P\right)R}{-28Px-24P}=\frac{15x-18}{-28Px-24P}$$

Dividing by -24P-28xP undoes the multiplication by -24P-28xP.

$$R=\frac{15x-18}{-28Px-24P}$$

Divide 15x-18 by -24P-28xP.

$$R=-\frac{3\left(5x-6\right)}{4P\left(7x+6\right)}$$

Solve for P

$$\left\{\begin{matrix}P=-\frac{3\left(5x-6\right)}{4R\left(7x+6\right)}\text{, }&x\neq -\frac{6}{7}\text{ and }R\neq 0\\P\in \mathrm{R}\text{, }&x=\frac{6}{5}\text{ and }R=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$6RP\times \frac{2}{3}\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

Multiply 6 and \frac{2}{3} to get 4.

$$4RP\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

To find the opposite of \frac{x}{3}+6, find the opposite of each term.

$$4RP\left(2-\frac{x}{3}-6-2\left(x-1\right)\right)=5x-6$$

Subtract 6 from 2 to get -4.

$$4RP\left(-4-\frac{x}{3}-2\left(x-1\right)\right)=5x-6$$

Use the distributive property to multiply -2 by x-1.

$$4RP\left(-4-\frac{x}{3}-2x+2\right)=5x-6$$

Add -4 and 2 to get -2.

$$4RP\left(-2-\frac{x}{3}-2x\right)=5x-6$$

Use the distributive property to multiply 4RP by -2-\frac{x}{3}-2x.

$$-8PR-4PR\times \frac{x}{3}-8PRx=5x-6$$

Express -4\times \frac{x}{3} as a single fraction.

$$-8PR+\frac{-4x}{3}PR-8PRx=5x-6$$

Express \frac{-4x}{3}P as a single fraction.

$$-8PR+\frac{-4xP}{3}R-8PRx=5x-6$$

Express \frac{-4xP}{3}R as a single fraction.

$$-8PR+\frac{-4xPR}{3}-8PRx=5x-6$$

Multiply both sides of the equation by 3.

$$-24PR-4xPR-24PRx=15x-18$$

Combine -4xPR and -24PRx to get -28xPR.

$$-24PR-28xPR=15x-18$$

Combine all terms containing P.

$$\left(-24R-28xR\right)P=15x-18$$

The equation is in standard form.

$$\left(-28Rx-24R\right)P=15x-18$$

Divide both sides by -24R-28xR.

$$\frac{\left(-28Rx-24R\right)P}{-28Rx-24R}=\frac{15x-18}{-28Rx-24R}$$

Dividing by -24R-28xR undoes the multiplication by -24R-28xR.

$$P=\frac{15x-18}{-28Rx-24R}$$

Divide 15x-18 by -24R-28xR.

$$P=-\frac{3\left(5x-6\right)}{4R\left(7x+6\right)}$$

Solve for R

$$\left\{\begin{matrix}R=-\frac{3\left(5x-6\right)}{4P\left(7x+6\right)}\text{, }&x\neq -\frac{6}{7}\text{ and }P\neq 0\\R\in \mathrm{R}\text{, }&x=\frac{6}{5}\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 3,6.

$$6RP\times \frac{2}{3}\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

Multiply 6 and \frac{2}{3} to get 4.

$$4RP\left(2-\left(\frac{x}{3}+6\right)-2\left(x-1\right)\right)=5x-6$$

To find the opposite of \frac{x}{3}+6, find the opposite of each term.

$$4RP\left(2-\frac{x}{3}-6-2\left(x-1\right)\right)=5x-6$$

Subtract 6 from 2 to get -4.

$$4RP\left(-4-\frac{x}{3}-2\left(x-1\right)\right)=5x-6$$

Use the distributive property to multiply -2 by x-1.

$$4RP\left(-4-\frac{x}{3}-2x+2\right)=5x-6$$

Add -4 and 2 to get -2.

$$4RP\left(-2-\frac{x}{3}-2x\right)=5x-6$$

Use the distributive property to multiply 4RP by -2-\frac{x}{3}-2x.

$$-8PR-4PR\times \frac{x}{3}-8PRx=5x-6$$

Express -4\times \frac{x}{3} as a single fraction.

$$-8PR+\frac{-4x}{3}PR-8PRx=5x-6$$

Express \frac{-4x}{3}P as a single fraction.

$$-8PR+\frac{-4xP}{3}R-8PRx=5x-6$$

Express \frac{-4xP}{3}R as a single fraction.

$$-8PR+\frac{-4xPR}{3}-8PRx=5x-6$$

Multiply both sides of the equation by 3.

$$-24PR-4xPR-24PRx=15x-18$$

Combine -4xPR and -24PRx to get -28xPR.

$$-24PR-28xPR=15x-18$$

Combine all terms containing R.

$$\left(-24P-28xP\right)R=15x-18$$

The equation is in standard form.

$$\left(-28Px-24P\right)R=15x-18$$

Divide both sides by -24P-28xP.

$$\frac{\left(-28Px-24P\right)R}{-28Px-24P}=\frac{15x-18}{-28Px-24P}$$

Dividing by -24P-28xP undoes the multiplication by -24P-28xP.

$$R=\frac{15x-18}{-28Px-24P}$$

Divide 15x-18 by -24P-28xP.

$$R=-\frac{3\left(5x-6\right)}{4P\left(7x+6\right)}$$