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

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


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

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

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

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

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

Solving
-16 + 12x + -2x2 = 2

Solving for variable 'x'.

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

Combine like terms: -16 + -2 = -18
-18 + 12x + -2x2 = 2 + -2

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 6x + -1x2) = 0

Factor a trinomial.
2((-3 + x)(3 + -1x)) = 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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {3, 3}

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