(2x-4)(x+6)=0

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Solution for (2x-4)(x+6)=0 equation:


Simplifying
(2x + -4)(x + 6) = 0

Reorder the terms:
(-4 + 2x)(x + 6) = 0

Reorder the terms:
(-4 + 2x)(6 + x) = 0

Multiply (-4 + 2x) * (6 + x)
(-4(6 + x) + 2x * (6 + x)) = 0
((6 * -4 + x * -4) + 2x * (6 + x)) = 0
((-24 + -4x) + 2x * (6 + x)) = 0
(-24 + -4x + (6 * 2x + x * 2x)) = 0
(-24 + -4x + (12x + 2x2)) = 0

Combine like terms: -4x + 12x = 8x
(-24 + 8x + 2x2) = 0

Solving
-24 + 8x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4x + x2) = 0

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

Ignore the factor 2.

Subproblem 1

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

Subproblem 2

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

Solution

x = {-6, 2}

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