Solve for x 3(x-6)=8x-3(3x+7)

$3 (x - 6) = 8 x - 3 (3 x + 7)$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$8 x - 3 (3 x + 7) = 3 (x - 6)$

Simplify $8 x - 3 (3 x + 7)$ .

Simplify each term.

Apply the distributive property.

$8 x - 3 (3 x) - 3 \cdot 7 = 3 (x - 6)$

Multiply $3$ by $- 3$ .

$8 x - 9 x - 3 \cdot 7 = 3 (x - 6)$

Multiply $- 3$ by $7$ .

$8 x - 9 x - 21 = 3 (x - 6)$

Subtract $9 x$ from $8 x$ .

$- x - 21 = 3 (x - 6)$

Simplify $3 (x - 6)$ .

Apply the distributive property.

$- x - 21 = 3 x + 3 \cdot - 6$

Multiply $3$ by $- 6$ .

$- x - 21 = 3 x - 18$

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

Subtract $3 x$ from both sides of the equation.

$- x - 21 - 3 x = - 18$

Subtract $3 x$ from $- x$ .

$- 4 x - 21 = - 18$

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

Add $21$ to both sides of the equation.

$- 4 x = - 18 + 21$

Add $- 18$ and $21$ .

$- 4 x = 3$

Divide each term in $- 4 x = 3$ by $- 4$ and simplify.

Divide each term in $- 4 x = 3$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Divide $x$ by $1$ .

$x = \frac{3}{- 4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{3}{4}$

Decimal Form:

$x = - 0.75$