5x(4x+12)(3x-15)=0

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Solution for 5x(4x+12)(3x-15)=0 equation: 


Simplifying
5x(4x + 12)(3x + -15) = 0

Reorder the terms:
5x(12 + 4x)(3x + -15) = 0

Reorder the terms:
5x(12 + 4x)(-15 + 3x) = 0

Multiply (12 + 4x) * (-15 + 3x)
5x(12(-15 + 3x) + 4x * (-15 + 3x)) = 0
5x((-15 * 12 + 3x * 12) + 4x * (-15 + 3x)) = 0
5x((-180 + 36x) + 4x * (-15 + 3x)) = 0
5x(-180 + 36x + (-15 * 4x + 3x * 4x)) = 0
5x(-180 + 36x + (-60x + 12x2)) = 0

Combine like terms: 36x + -60x = -24x
5x(-180 + -24x + 12x2) = 0
(-180 * 5x + -24x * 5x + 12x2 * 5x) = 0
(-900x + -120x2 + 60x3) = 0

Solving
-900x + -120x2 + 60x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '60x'.
60x(-15 + -2x + x2) = 0

Factor a trinomial.
60x((-3 + -1x)(5 + -1x)) = 0

Ignore the factor 60.

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 + -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 3
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
Solution
x = {0, -3, 5}

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