Solve for x 6(x-1)=9(x+2)

$6 (x - 1) = 9 (x + 2)$

Step 1

Simplify $6 (x - 1)$ .

Rewrite.

$0 + 0 + 6 (x - 1) = 9 (x + 2)$

Simplify by adding zeros.

$6 (x - 1) = 9 (x + 2)$

Apply the distributive property.

$6 x + 6 \cdot - 1 = 9 (x + 2)$

Multiply $6$ by $- 1$ .

$6 x - 6 = 9 (x + 2)$

Step 2

Simplify $9 (x + 2)$ .

Apply the distributive property.

$6 x - 6 = 9 x + 9 \cdot 2$

Multiply $9$ by $2$ .

$6 x - 6 = 9 x + 18$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $9 x$ from both sides of the equation.

$6 x - 6 - 9 x = 18$

Subtract $9 x$ from $6 x$ .

$- 3 x - 6 = 18$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $6$ to both sides of the equation.

$- 3 x = 18 + 6$

Add $18$ and $6$ .

$- 3 x = 24$

Step 5

Divide each term in $- 3 x = 24$ by $- 3$ and simplify.

Divide each term in $- 3 x = 24$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{24}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{24}{- 3}$

Divide $x$ by $1$ .

$x = \frac{24}{- 3}$

Simplify the right side.

Divide $24$ by $- 3$ .

$x = - 8$