(2x-6)(2x+10)=0

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Solution for (2x-6)(2x+10)=0 equation:


Simplifying
(2x + -6)(2x + 10) = 0

Reorder the terms:
(-6 + 2x)(2x + 10) = 0

Reorder the terms:
(-6 + 2x)(10 + 2x) = 0

Multiply (-6 + 2x) * (10 + 2x)
(-6(10 + 2x) + 2x * (10 + 2x)) = 0
((10 * -6 + 2x * -6) + 2x * (10 + 2x)) = 0
((-60 + -12x) + 2x * (10 + 2x)) = 0
(-60 + -12x + (10 * 2x + 2x * 2x)) = 0
(-60 + -12x + (20x + 4x2)) = 0

Combine like terms: -12x + 20x = 8x
(-60 + 8x + 4x2) = 0

Solving
-60 + 8x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-15 + 2x + x2) = 0

Factor a trinomial.
4((-5 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5

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 = {-5, 3}

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