Solve for x 4(x-3)-(x+6)=3(x-6)

$4 (x - 3) - (x + 6) = 3 (x - 6)$

Simplify $4 (x - 3) - (x + 6)$ .

Simplify each term.

Apply the distributive property.

$4 x + 4 \cdot - 3 - (x + 6) = 3 (x - 6)$

Multiply $4$ by $- 3$ .

$4 x - 12 - (x + 6) = 3 (x - 6)$

Apply the distributive property.

$4 x - 12 - x - 1 \cdot 6 = 3 (x - 6)$

Multiply $- 1$ by $6$ .

$4 x - 12 - x - 6 = 3 (x - 6)$

Simplify by adding terms.

Subtract $x$ from $4 x$ .

$3 x - 12 - 6 = 3 (x - 6)$

Subtract $6$ from $- 12$ .

$3 x - 18 = 3 (x - 6)$

Simplify $3 (x - 6)$ .

Apply the distributive property.

$3 x - 18 = 3 x + 3 \cdot - 6$

Multiply $3$ by $- 6$ .

$3 x - 18 = 3 x - 18$

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

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

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

Combine the opposite terms in $3 x - 18 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 18 = - 18$

Subtract $18$ from $0$ .

$- 18 = - 18$

Since $- 18 = - 18$ , the equation will always be true for any value of $x$ .

All real numbers

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$