5x(2x-6)(-4x-12)=0

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Solution for 5x(2x-6)(-4x-12)=0 equation: 


Simplifying
5x(2x + -6)(-4x + -12) = 0

Reorder the terms:
5x(-6 + 2x)(-4x + -12) = 0

Reorder the terms:
5x(-6 + 2x)(-12 + -4x) = 0

Multiply (-6 + 2x) * (-12 + -4x)
5x(-6(-12 + -4x) + 2x * (-12 + -4x)) = 0
5x((-12 * -6 + -4x * -6) + 2x * (-12 + -4x)) = 0
5x((72 + 24x) + 2x * (-12 + -4x)) = 0
5x(72 + 24x + (-12 * 2x + -4x * 2x)) = 0
5x(72 + 24x + (-24x + -8x2)) = 0

Combine like terms: 24x + -24x = 0
5x(72 + 0 + -8x2) = 0
5x(72 + -8x2) = 0
(72 * 5x + -8x2 * 5x) = 0
(360x + -40x3) = 0

Solving
360x + -40x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '40x'.
40x(9 + -1x2) = 0

Factor a difference between two squares.
40x((3 + x)(3 + -1x)) = 0

Ignore the factor 40.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

Subproblem 3
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 = {0, -3, 3}

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