Solve for x 3(x+5)+6x=-3(1-3x)+18

$3 (x + 5) + 6 x = - 3 (1 - 3 x) + 18$

Simplify $3 (x + 5) + 6 x$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 5 + 6 x = - 3 (1 - 3 x) + 18$

Multiply $3$ by $5$ .

$3 x + 15 + 6 x = - 3 (1 - 3 x) + 18$

Add $3 x$ and $6 x$ .

$9 x + 15 = - 3 (1 - 3 x) + 18$

Simplify $- 3 (1 - 3 x) + 18$ .

Simplify each term.

Apply the distributive property.

$9 x + 15 = - 3 \cdot 1 - 3 (- 3 x) + 18$

Multiply $- 3$ by $1$ .

$9 x + 15 = - 3 - 3 (- 3 x) + 18$

Multiply $- 3$ by $- 3$ .

$9 x + 15 = - 3 + 9 x + 18$

Add $- 3$ and $18$ .

$9 x + 15 = 9 x + 15$

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

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

$9 x + 15 - 9 x = 15$

Combine the opposite terms in $9 x + 15 - 9 x$ .

Subtract $9 x$ from $9 x$ .

$0 + 15 = 15$

Add $0$ and $15$ .

$15 = 15$

Since $15 = 15$ , 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:

$(- \infty, \infty)$