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

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


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

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

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

Reorder the terms for easier multiplication:
3(-6 + 4x)(-6 + x) = 0

Multiply (-6 + 4x) * (-6 + x)
3(-6(-6 + x) + 4x * (-6 + x)) = 0
3((-6 * -6 + x * -6) + 4x * (-6 + x)) = 0
3((36 + -6x) + 4x * (-6 + x)) = 0
3(36 + -6x + (-6 * 4x + x * 4x)) = 0
3(36 + -6x + (-24x + 4x2)) = 0

Combine like terms: -6x + -24x = -30x
3(36 + -30x + 4x2) = 0
(36 * 3 + -30x * 3 + 4x2 * 3) = 0
(108 + -90x + 12x2) = 0

Solving
108 + -90x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(18 + -15x + 2x2) = 0

Factor a trinomial.
6((3 + -2x)(6 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

Subproblem 2

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

Solution

x = {1.5, 6}

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