-2x(x+3)=-2x-6

Solution for -2x(x+3)=-2x-6 equation:

Simplifying
-2x(x + 3) = -2x + -6

Reorder the terms:
-2x(3 + x) = -2x + -6
(3 * -2x + x * -2x) = -2x + -6
(-6x + -2x2) = -2x + -6

Reorder the terms:
-6x + -2x2 = -6 + -2x

Solving
-6x + -2x2 = -6 + -2x

Solving for variable 'x'.

Reorder the terms:
6 + -6x + 2x + -2x2 = -6 + -2x + 6 + 2x

Combine like terms: -6x + 2x = -4x
6 + -4x + -2x2 = -6 + -2x + 6 + 2x

Reorder the terms:
6 + -4x + -2x2 = -6 + 6 + -2x + 2x

Combine like terms: -6 + 6 = 0
6 + -4x + -2x2 = 0 + -2x + 2x
6 + -4x + -2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -2x + -1x2) = 0

Factor a trinomial.
2((1 + -1x)(3 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}