Solve [12x-6(a-x)]-3x=3b-3(3ax+9)

$$[ 12 x - 6 ( a - x ) ] - 3 x = 3 b - 3 ( 3 a x + 9 )$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{5x-b+9}{3x-2}\text{, }&x\neq \frac{2}{3}\\a\in \mathrm{C}\text{, }&x=\frac{2}{3}\text{ and }b=\frac{37}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -6 by a-x.

$$12x-6a+6x-3x=3b-3\left(3ax+9\right)$$

Combine 12x and 6x to get 18x.

$$18x-6a-3x=3b-3\left(3ax+9\right)$$

Combine 18x and -3x to get 15x.

$$15x-6a=3b-3\left(3ax+9\right)$$

Use the distributive property to multiply -3 by 3ax+9.

$$15x-6a=3b-9xa-27$$

Add 9xa to both sides.

$$15x-6a+9xa=3b-27$$

Subtract 15x from both sides.

$$-6a+9xa=3b-27-15x$$

Combine all terms containing a.

$$\left(-6+9x\right)a=3b-27-15x$$

The equation is in standard form.

$$\left(9x-6\right)a=-15x+3b-27$$

Divide both sides by 9x-6.

$$\frac{\left(9x-6\right)a}{9x-6}=\frac{-15x+3b-27}{9x-6}$$

Dividing by 9x-6 undoes the multiplication by 9x-6.

$$a=\frac{-15x+3b-27}{9x-6}$$

Divide -27+3b-15x by 9x-6.

$$a=\frac{-5x+b-9}{3x-2}$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{5x-b+9}{3x-2}\text{, }&x\neq \frac{2}{3}\\a\in \mathrm{R}\text{, }&x=\frac{2}{3}\text{ and }b=\frac{37}{3}\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply -6 by a-x.

$$12x-6a+6x-3x=3b-3\left(3ax+9\right)$$

Combine 12x and 6x to get 18x.

$$18x-6a-3x=3b-3\left(3ax+9\right)$$

Combine 18x and -3x to get 15x.

$$15x-6a=3b-3\left(3ax+9\right)$$

Use the distributive property to multiply -3 by 3ax+9.

$$15x-6a=3b-9xa-27$$

Add 9xa to both sides.

$$15x-6a+9xa=3b-27$$

Subtract 15x from both sides.

$$-6a+9xa=3b-27-15x$$

Combine all terms containing a.

$$\left(-6+9x\right)a=3b-27-15x$$

The equation is in standard form.

$$\left(9x-6\right)a=-15x+3b-27$$

Divide both sides by 9x-6.

$$\frac{\left(9x-6\right)a}{9x-6}=\frac{-15x+3b-27}{9x-6}$$

Dividing by 9x-6 undoes the multiplication by 9x-6.

$$a=\frac{-15x+3b-27}{9x-6}$$

Divide -27+3b-15x by 9x-6.

$$a=\frac{-5x+b-9}{3x-2}$$

Solve for b

$$b=3ax+5x-2a+9$$

Steps for Solving Linear Equation

Use the distributive property to multiply -6 by a-x.

$$12x-6a+6x-3x=3b-3\left(3ax+9\right)$$

Combine 12x and 6x to get 18x.

$$18x-6a-3x=3b-3\left(3ax+9\right)$$

Combine 18x and -3x to get 15x.

$$15x-6a=3b-3\left(3ax+9\right)$$

Use the distributive property to multiply -3 by 3ax+9.

$$15x-6a=3b-9ax-27$$

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

$$3b-9ax-27=15x-6a$$

Add 9ax to both sides.

$$3b-27=15x-6a+9ax$$

Add 27 to both sides.

$$3b=15x-6a+9ax+27$$

The equation is in standard form.

$$3b=9ax+15x-6a+27$$

Divide both sides by 3.

$$\frac{3b}{3}=\frac{9ax+15x-6a+27}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$b=\frac{9ax+15x-6a+27}{3}$$

Divide 15x-6a+9ax+27 by 3.

$$b=3ax+5x-2a+9$$