Solve p/I:y-y-1/2=2-y+2/6quad5

$$\frac { p } { I } : y - \frac { y - 1 } { 2 } = 2 - \frac { y + 2 } { 6 } \quad 5$$

Solve for I

$$\left\{\begin{matrix}I=-\frac{6p}{y\left(2y+1\right)}\text{, }&p\neq 0\text{ and }y\neq -\frac{1}{2}\text{ and }y\neq 0\\I\neq 0\text{, }&p=0\text{ and }y=-\frac{1}{2}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6y, the least common multiple of y,2,6.

$$6\times \frac{p}{I}-3y\left(y-1\right)=6y\times 2-y\left(y+2\right)\times 5$$

Express 6\times \frac{p}{I} as a single fraction.

$$\frac{6p}{I}-3y\left(y-1\right)=6y\times 2-y\left(y+2\right)\times 5$$

Use the distributive property to multiply 3y by y-1.

$$\frac{6p}{I}-\left(3y^{2}-3y\right)=6y\times 2-y\left(y+2\right)\times 5$$

To find the opposite of 3y^{2}-3y, find the opposite of each term.

$$\frac{6p}{I}-3y^{2}+3y=6y\times 2-y\left(y+2\right)\times 5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y^{2}+3y times \frac{I}{I}.

$$\frac{6p}{I}+\frac{\left(-3y^{2}+3y\right)I}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Since \frac{6p}{I} and \frac{\left(-3y^{2}+3y\right)I}{I} have the same denominator, add them by adding their numerators.

$$\frac{6p+\left(-3y^{2}+3y\right)I}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Do the multiplications in 6p+\left(-3y^{2}+3y\right)I.

$$\frac{6p-3y^{2}I+3yI}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Multiply 6 and 2 to get 12.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-y\left(y+2\right)\times 5$$

Use the distributive property to multiply y by y+2.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-\left(y^{2}+2y\right)\times 5$$

Use the distributive property to multiply y^{2}+2y by 5.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-\left(5y^{2}+10y\right)$$

To find the opposite of 5y^{2}+10y, find the opposite of each term.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-5y^{2}-10y$$

Combine 12y and -10y to get 2y.

$$\frac{6p-3y^{2}I+3yI}{I}=2y-5y^{2}$$

Variable I cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by I.

$$6p-3y^{2}I+3yI=2yI-5y^{2}I$$

Subtract 2yI from both sides.

$$6p-3y^{2}I+3yI-2yI=-5y^{2}I$$

Combine 3yI and -2yI to get yI.

$$6p-3y^{2}I+yI=-5y^{2}I$$

Add 5y^{2}I to both sides.

$$6p-3y^{2}I+yI+5y^{2}I=0$$

Combine -3y^{2}I and 5y^{2}I to get 2y^{2}I.

$$6p+2y^{2}I+yI=0$$

Subtract 6p from both sides. Anything subtracted from zero gives its negation.

$$2y^{2}I+yI=-6p$$

Combine all terms containing I.

$$\left(2y^{2}+y\right)I=-6p$$

Divide both sides by y+2y^{2}.

$$\frac{\left(2y^{2}+y\right)I}{2y^{2}+y}=-\frac{6p}{2y^{2}+y}$$

Dividing by y+2y^{2} undoes the multiplication by y+2y^{2}.

$$I=-\frac{6p}{2y^{2}+y}$$

Divide -6p by y+2y^{2}.

$$I=-\frac{6p}{y\left(2y+1\right)}$$

Variable I cannot be equal to 0.

$$I=-\frac{6p}{y\left(2y+1\right)}\text{, }I\neq 0$$

Solve for p

$$p=-\frac{Iy\left(2y+1\right)}{6}$$

$$I\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6y, the least common multiple of y,2,6.

$$6\times \frac{p}{I}-3y\left(y-1\right)=6y\times 2-y\left(y+2\right)\times 5$$

Express 6\times \frac{p}{I} as a single fraction.

$$\frac{6p}{I}-3y\left(y-1\right)=6y\times 2-y\left(y+2\right)\times 5$$

Use the distributive property to multiply 3y by y-1.

$$\frac{6p}{I}-\left(3y^{2}-3y\right)=6y\times 2-y\left(y+2\right)\times 5$$

To find the opposite of 3y^{2}-3y, find the opposite of each term.

$$\frac{6p}{I}-3y^{2}+3y=6y\times 2-y\left(y+2\right)\times 5$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -3y^{2}+3y times \frac{I}{I}.

$$\frac{6p}{I}+\frac{\left(-3y^{2}+3y\right)I}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Since \frac{6p}{I} and \frac{\left(-3y^{2}+3y\right)I}{I} have the same denominator, add them by adding their numerators.

$$\frac{6p+\left(-3y^{2}+3y\right)I}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Do the multiplications in 6p+\left(-3y^{2}+3y\right)I.

$$\frac{6p-3y^{2}I+3yI}{I}=6y\times 2-y\left(y+2\right)\times 5$$

Multiply 6 and 2 to get 12.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-y\left(y+2\right)\times 5$$

Use the distributive property to multiply y by y+2.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-\left(y^{2}+2y\right)\times 5$$

Use the distributive property to multiply y^{2}+2y by 5.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-\left(5y^{2}+10y\right)$$

To find the opposite of 5y^{2}+10y, find the opposite of each term.

$$\frac{6p-3y^{2}I+3yI}{I}=12y-5y^{2}-10y$$

Combine 12y and -10y to get 2y.

$$\frac{6p-3y^{2}I+3yI}{I}=2y-5y^{2}$$

Multiply both sides of the equation by I.

$$6p-3y^{2}I+3yI=2yI-5y^{2}I$$

Add 3y^{2}I to both sides.

$$6p+3yI=2yI-5y^{2}I+3y^{2}I$$

Combine -5y^{2}I and 3y^{2}I to get -2y^{2}I.

$$6p+3yI=2yI-2y^{2}I$$

Subtract 3yI from both sides.

$$6p=2yI-2y^{2}I-3yI$$

Combine 2yI and -3yI to get -yI.

$$6p=-yI-2y^{2}I$$

The equation is in standard form.

$$6p=-2Iy^{2}-Iy$$

Divide both sides by 6.

$$\frac{6p}{6}=-\frac{Iy\left(2y+1\right)}{6}$$

Dividing by 6 undoes the multiplication by 6.

$$p=-\frac{Iy\left(2y+1\right)}{6}$$