Solve a(2-x)+3(x+6)=10-4(6+bx)

$$a ( 2 - x ) + 3 ( x + 6 ) = 10 - 4 ( 6 + b x )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{4bx+3x+32}{2-x}\text{, }&x\neq 2\\a\in \mathrm{C}\text{, }&b=-\frac{19}{4}\text{ and }x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2a-ax+3\left(x+6\right)=10-4\left(6+bx\right)$$

Use the distributive property to multiply 3 by x+6.

$$2a-ax+3x+18=10-4\left(6+bx\right)$$

Use the distributive property to multiply -4 by 6+bx.

$$2a-ax+3x+18=10-24-4bx$$

Subtract 24 from 10 to get -14.

$$2a-ax+3x+18=-14-4bx$$

Subtract 3x from both sides.

$$2a-ax+18=-14-4bx-3x$$

Subtract 18 from both sides.

$$2a-ax=-14-4bx-3x-18$$

Subtract 18 from -14 to get -32.

$$2a-ax=-32-4bx-3x$$

Combine all terms containing a.

$$\left(2-x\right)a=-32-4bx-3x$$

The equation is in standard form.

$$\left(2-x\right)a=-4bx-3x-32$$

Divide both sides by 2-x.

$$\frac{\left(2-x\right)a}{2-x}=\frac{-4bx-3x-32}{2-x}$$

Dividing by 2-x undoes the multiplication by 2-x.

$$a=\frac{-4bx-3x-32}{2-x}$$

Divide -32-4bx-3x by 2-x.

$$a=-\frac{4bx+3x+32}{2-x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\frac{ax-3x-2a-32}{4x}\text{, }&x\neq 0\\b\in \mathrm{C}\text{, }&x=0\text{ and }a=-16\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2a-ax+3\left(x+6\right)=10-4\left(6+bx\right)$$

Use the distributive property to multiply 3 by x+6.

$$2a-ax+3x+18=10-4\left(6+bx\right)$$

Use the distributive property to multiply -4 by 6+bx.

$$2a-ax+3x+18=10-24-4bx$$

Subtract 24 from 10 to get -14.

$$2a-ax+3x+18=-14-4bx$$

Swap sides so that all variable terms are on the left hand side.

$$-14-4bx=2a-ax+3x+18$$

Add 14 to both sides.

$$-4bx=2a-ax+3x+18+14$$

Add 18 and 14 to get 32.

$$-4bx=2a-ax+3x+32$$

The equation is in standard form.

$$\left(-4x\right)b=32+2a+3x-ax$$

Divide both sides by -4x.

$$\frac{\left(-4x\right)b}{-4x}=\frac{32+2a+3x-ax}{-4x}$$

Dividing by -4x undoes the multiplication by -4x.

$$b=\frac{32+2a+3x-ax}{-4x}$$

Divide 32+2a-ax+3x by -4x.

$$b=\frac{a}{4}-\frac{\frac{a}{2}+8}{x}-\frac{3}{4}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{4bx+3x+32}{2-x}\text{, }&x\neq 2\\a\in \mathrm{R}\text{, }&b=-\frac{19}{4}\text{ and }x=2\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2a-ax+3\left(x+6\right)=10-4\left(6+bx\right)$$

Use the distributive property to multiply 3 by x+6.

$$2a-ax+3x+18=10-4\left(6+bx\right)$$

Use the distributive property to multiply -4 by 6+bx.

$$2a-ax+3x+18=10-24-4bx$$

Subtract 24 from 10 to get -14.

$$2a-ax+3x+18=-14-4bx$$

Subtract 3x from both sides.

$$2a-ax+18=-14-4bx-3x$$

Subtract 18 from both sides.

$$2a-ax=-14-4bx-3x-18$$

Subtract 18 from -14 to get -32.

$$2a-ax=-32-4bx-3x$$

Combine all terms containing a.

$$\left(2-x\right)a=-32-4bx-3x$$

The equation is in standard form.

$$\left(2-x\right)a=-4bx-3x-32$$

Divide both sides by 2-x.

$$\frac{\left(2-x\right)a}{2-x}=\frac{-4bx-3x-32}{2-x}$$

Dividing by 2-x undoes the multiplication by 2-x.

$$a=\frac{-4bx-3x-32}{2-x}$$

Divide -32-4bx-3x by 2-x.

$$a=-\frac{4bx+3x+32}{2-x}$$

Solve for b

$$\left\{\begin{matrix}b=\frac{ax-3x-2a-32}{4x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&x=0\text{ and }a=-16\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$2a-ax+3\left(x+6\right)=10-4\left(6+bx\right)$$

Use the distributive property to multiply 3 by x+6.

$$2a-ax+3x+18=10-4\left(6+bx\right)$$

Use the distributive property to multiply -4 by 6+bx.

$$2a-ax+3x+18=10-24-4bx$$

Subtract 24 from 10 to get -14.

$$2a-ax+3x+18=-14-4bx$$

Swap sides so that all variable terms are on the left hand side.

$$-14-4bx=2a-ax+3x+18$$

Add 14 to both sides.

$$-4bx=2a-ax+3x+18+14$$

Add 18 and 14 to get 32.

$$-4bx=2a-ax+3x+32$$

The equation is in standard form.

$$\left(-4x\right)b=32+2a+3x-ax$$

Divide both sides by -4x.

$$\frac{\left(-4x\right)b}{-4x}=\frac{32+2a+3x-ax}{-4x}$$

Dividing by -4x undoes the multiplication by -4x.

$$b=\frac{32+2a+3x-ax}{-4x}$$

Divide 2a-ax+3x+32 by -4x.

$$b=\frac{a}{4}-\frac{\frac{a}{2}+8}{x}-\frac{3}{4}$$