-2x(4-x)=12+2x

Solution for -2x(4-x)=12+2x equation:

Simplifying
-2x(4 + -1x) = 12 + 2x
(4 * -2x + -1x * -2x) = 12 + 2x
(-8x + 2x2) = 12 + 2x

Solving
-8x + 2x2 = 12 + 2x

Solving for variable 'x'.

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

Combine like terms: -8x + -2x = -10x
-12 + -10x + 2x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-12 + -10x + 2x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-12 + -10x + 2x2 = 0 + 2x + -2x
-12 + -10x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + -10x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5x + x2) = 0

Factor a trinomial.
2((-1 + -1x)(6 + -1x)) = 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}