(-6+6x)-(2x^2-4)=2

Solution for (-6+6x)-(2x^2-4)=2 equation:

Simplifying
(-6 + 6x) + -1(2x2 + -4) = 2

Remove parenthesis around (-6 + 6x)
-6 + 6x + -1(2x2 + -4) = 2

Reorder the terms:
-6 + 6x + -1(-4 + 2x2) = 2
-6 + 6x + (-4 * -1 + 2x2 * -1) = 2
-6 + 6x + (4 + -2x2) = 2

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Subproblem 2
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
Solution
x = {2, 1}