(2x-12)x(3x+15)=0

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Solution for (2x-12)x(3x+15)=0 equation: 


Simplifying
(2x + -12) * x(3x + 15) = 0

Reorder the terms:
(-12 + 2x) * x(3x + 15) = 0

Reorder the terms:
(-12 + 2x) * x(15 + 3x) = 0

Reorder the terms for easier multiplication:
x(-12 + 2x)(15 + 3x) = 0

Multiply (-12 + 2x) * (15 + 3x)
x(-12(15 + 3x) + 2x * (15 + 3x)) = 0
x((15 * -12 + 3x * -12) + 2x * (15 + 3x)) = 0
x((-180 + -36x) + 2x * (15 + 3x)) = 0
x(-180 + -36x + (15 * 2x + 3x * 2x)) = 0
x(-180 + -36x + (30x + 6x2)) = 0

Combine like terms: -36x + 30x = -6x
x(-180 + -6x + 6x2) = 0
(-180 * x + -6x * x + 6x2 * x) = 0
(-180x + -6x2 + 6x3) = 0

Solving
-180x + -6x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-30 + -1x + x2) = 0

Factor a trinomial.
6x((-5 + -1x)(6 + -1x)) = 0

Ignore the factor 6.

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 '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 3
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 = {0, -5, 6}

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