(2x-6)(3x+12)=0

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Solution for (2x-6)(3x+12)=0 equation:


Simplifying
(2x + -6)(3x + 12) = 0

Reorder the terms:
(-6 + 2x)(3x + 12) = 0

Reorder the terms:
(-6 + 2x)(12 + 3x) = 0

Multiply (-6 + 2x) * (12 + 3x)
(-6(12 + 3x) + 2x * (12 + 3x)) = 0
((12 * -6 + 3x * -6) + 2x * (12 + 3x)) = 0
((-72 + -18x) + 2x * (12 + 3x)) = 0
(-72 + -18x + (12 * 2x + 3x * 2x)) = 0
(-72 + -18x + (24x + 6x2)) = 0

Combine like terms: -18x + 24x = 6x
(-72 + 6x + 6x2) = 0

Solving
-72 + 6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-12 + x + x2) = 0

Factor a trinomial.
6((-4 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

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 = {-4, 3}

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