2(x-6)(x-2)=24

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Solution for 2(x-6)(x-2)=24 equation: 


Simplifying
2(x + -6)(x + -2) = 24

Reorder the terms:
2(-6 + x)(x + -2) = 24

Reorder the terms:
2(-6 + x)(-2 + x) = 24

Multiply (-6 + x) * (-2 + x)
2(-6(-2 + x) + x(-2 + x)) = 24
2((-2 * -6 + x * -6) + x(-2 + x)) = 24
2((12 + -6x) + x(-2 + x)) = 24
2(12 + -6x + (-2 * x + x * x)) = 24
2(12 + -6x + (-2x + x2)) = 24

Combine like terms: -6x + -2x = -8x
2(12 + -8x + x2) = 24
(12 * 2 + -8x * 2 + x2 * 2) = 24
(24 + -16x + 2x2) = 24

Add '-24' to each side of the equation.
24 + -16x + -24 + 2x2 = 24 + -24

Reorder the terms:
24 + -24 + -16x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
0 + -16x + 2x2 = 24 + -24
-16x + 2x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-16x + 2x2 = 0

Solving
-16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8 + x) = 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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {0, 8}

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