Solve for x 2(9-3(-2x-4))=12x+42

$2 (9 - 3 (- 2 x - 4)) = 12 x + 42$

Step 1

Simplify $2 (9 - 3 (- 2 x - 4))$ .

Rewrite.

$0 + 0 + 2 (9 - 3 (- 2 x - 4)) = 12 x + 42$

Simplify by adding zeros.

$2 (9 - 3 (- 2 x - 4)) = 12 x + 42$

Simplify each term.

Apply the distributive property.

$2 (9 - 3 (- 2 x) - 3 \cdot - 4) = 12 x + 42$

Multiply $- 2$ by $- 3$ .

$2 (9 + 6 x - 3 \cdot - 4) = 12 x + 42$

Multiply $- 3$ by $- 4$ .

$2 (9 + 6 x + 12) = 12 x + 42$

Simplify by multiplying through.

Add $9$ and $12$ .

$2 (6 x + 21) = 12 x + 42$

Apply the distributive property.

$2 (6 x) + 2 \cdot 21 = 12 x + 42$

Multiply.

Multiply $6$ by $2$ .

$12 x + 2 \cdot 21 = 12 x + 42$

Multiply $2$ by $21$ .

$12 x + 42 = 12 x + 42$

Step 2

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

Subtract $12 x$ from both sides of the equation.

$12 x + 42 - 12 x = 42$

Combine the opposite terms in $12 x + 42 - 12 x$ .

Subtract $12 x$ from $12 x$ .

$0 + 42 = 42$

Add $0$ and $42$ .

$42 = 42$

Step 3

Since $42 = 42$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$