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

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

Simplifying
2(x + 3) = -6x + 2(x2 + -2)

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

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

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

Solving
6 + 2x = -4 + -6x + 2x2

Solving for variable 'x'.

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

Combine like terms: 6 + 4 = 10
10 + 2x + 6x + -2x2 = -4 + -6x + 2x2 + 4 + 6x + -2x2

Combine like terms: 2x + 6x = 8x
10 + 8x + -2x2 = -4 + -6x + 2x2 + 4 + 6x + -2x2

Reorder the terms:
10 + 8x + -2x2 = -4 + 4 + -6x + 6x + 2x2 + -2x2

Combine like terms: -4 + 4 = 0
10 + 8x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2
10 + 8x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
10 + 8x + -2x2 = 0 + 2x2 + -2x2
10 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
10 + 8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 4x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(1 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {5, -1}