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

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Solution for 5(x+2)(x-6)=0 equation:


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

Reorder the terms:
5(2 + x)(x + -6) = 0

Reorder the terms:
5(2 + x)(-6 + x) = 0

Multiply (2 + x) * (-6 + x)
5(2(-6 + x) + x(-6 + x)) = 0
5((-6 * 2 + x * 2) + x(-6 + x)) = 0
5((-12 + 2x) + x(-6 + x)) = 0
5(-12 + 2x + (-6 * x + x * x)) = 0
5(-12 + 2x + (-6x + x2)) = 0

Combine like terms: 2x + -6x = -4x
5(-12 + -4x + x2) = 0
(-12 * 5 + -4x * 5 + x2 * 5) = 0
(-60 + -20x + 5x2) = 0

Solving
-60 + -20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -4x + x2) = 0

Factor a trinomial.
5((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 5.

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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