(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 = -42x
(72 + -42x + 6x2) = 0

Solving
72 + -42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -7x + x2) = 0

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

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

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

Solution

x = {3, 4}

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