2(x-6)(x-2)=0

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Solution for 2(x-6)(x-2)=0 equation:


Simplifying
2(x + -6)(x + -2) = 0

Reorder the terms:
2(-6 + x)(x + -2) = 0

Reorder the terms:
2(-6 + x)(-2 + x) = 0

Multiply (-6 + x) * (-2 + x)
2(-6(-2 + x) + x(-2 + x)) = 0
2((-2 * -6 + x * -6) + x(-2 + x)) = 0
2((12 + -6x) + x(-2 + x)) = 0
2(12 + -6x + (-2 * x + x * x)) = 0
2(12 + -6x + (-2x + x2)) = 0

Combine like terms: -6x + -2x = -8x
2(12 + -8x + x2) = 0
(12 * 2 + -8x * 2 + x2 * 2) = 0
(24 + -16x + 2x2) = 0

Solving
24 + -16x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -8x + x2) = 0

Factor a trinomial.
2((2 + -1x)(6 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

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 = {2, 6}

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