2(x+3)2-2x^2=18+12x

Solution for 2(x+3)2-2x^2=18+12x equation:

Simplifying
2(x + 3) * 2 + -2x2 = 18 + 12x

Reorder the terms:
2(3 + x) * 2 + -2x2 = 18 + 12x

Reorder the terms for easier multiplication:
2 * 2(3 + x) + -2x2 = 18 + 12x

Multiply 2 * 2
4(3 + x) + -2x2 = 18 + 12x
(3 * 4 + x * 4) + -2x2 = 18 + 12x
(12 + 4x) + -2x2 = 18 + 12x

Solving
12 + 4x + -2x2 = 18 + 12x

Solving for variable 'x'.

Reorder the terms:
12 + -18 + 4x + -12x + -2x2 = 18 + 12x + -18 + -12x

Combine like terms: 12 + -18 = -6
-6 + 4x + -12x + -2x2 = 18 + 12x + -18 + -12x

Combine like terms: 4x + -12x = -8x
-6 + -8x + -2x2 = 18 + 12x + -18 + -12x

Reorder the terms:
-6 + -8x + -2x2 = 18 + -18 + 12x + -12x

Combine like terms: 18 + -18 = 0
-6 + -8x + -2x2 = 0 + 12x + -12x
-6 + -8x + -2x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-6 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 4x + x2) = 0

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

Ignore the factor -2.
Subproblem 1
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
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 = {-3, -1}