(3x-6)(2x-4)=0

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Solution for (3x-6)(2x-4)=0 equation:


Simplifying
(3x + -6)(2x + -4) = 0

Reorder the terms:
(-6 + 3x)(2x + -4) = 0

Reorder the terms:
(-6 + 3x)(-4 + 2x) = 0

Multiply (-6 + 3x) * (-4 + 2x)
(-6(-4 + 2x) + 3x * (-4 + 2x)) = 0
((-4 * -6 + 2x * -6) + 3x * (-4 + 2x)) = 0
((24 + -12x) + 3x * (-4 + 2x)) = 0
(24 + -12x + (-4 * 3x + 2x * 3x)) = 0
(24 + -12x + (-12x + 6x2)) = 0

Combine like terms: -12x + -12x = -24x
(24 + -24x + 6x2) = 0

Solving
24 + -24x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(4 + -4x + x2) = 0

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

Ignore the factor 6.

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 '(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 = {2, 2}

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