-2[(x-2)(x-4)]=-16

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Solution for -2[(x-2)(x-4)]=-16 equation: 


Simplifying
-2[(x + -2)(x + -4)] = -16

Reorder the terms:
-2[(-2 + x)(x + -4)] = -16

Reorder the terms:
-2[(-2 + x)(-4 + x)] = -16

Multiply (-2 + x) * (-4 + x)
-2[(-2(-4 + x) + x(-4 + x))] = -16
-2[((-4 * -2 + x * -2) + x(-4 + x))] = -16
-2[((8 + -2x) + x(-4 + x))] = -16
-2[(8 + -2x + (-4 * x + x * x))] = -16
-2[(8 + -2x + (-4x + x2))] = -16

Combine like terms: -2x + -4x = -6x
-2[(8 + -6x + x2)] = -16
[8 * -2 + -6x * -2 + x2 * -2] = -16
[-16 + 12x + -2x2] = -16

Add '16' to each side of the equation.
-16 + 12x + 16 + -2x2 = -16 + 16

Reorder the terms:
-16 + 16 + 12x + -2x2 = -16 + 16

Combine like terms: -16 + 16 = 0
0 + 12x + -2x2 = -16 + 16
12x + -2x2 = -16 + 16

Combine like terms: -16 + 16 = 0
12x + -2x2 = 0

Solving
12x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(6 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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 = {0, 6}

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