Solve for x 2x-2(4x-3)=6-6x

$2 x - 2 (4 x - 3) = 6 - 6 x$

Step 1

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

Simplify each term.

Apply the distributive property.

$2 x - 2 (4 x) - 2 \cdot - 3 = 6 - 6 x$

Multiply $4$ by $- 2$ .

$2 x - 8 x - 2 \cdot - 3 = 6 - 6 x$

Multiply $- 2$ by $- 3$ .

$2 x - 8 x + 6 = 6 - 6 x$

Subtract $8 x$ from $2 x$ .

$- 6 x + 6 = 6 - 6 x$

Step 2

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

Add $6 x$ to both sides of the equation.

$- 6 x + 6 + 6 x = 6$

Combine the opposite terms in $- 6 x + 6 + 6 x$ .

Add $- 6 x$ and $6 x$ .

$0 + 6 = 6$

Add $0$ and $6$ .

$6 = 6$

Step 3

Since $6 = 6$ , 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:

$(- \infty, \infty)$