x(12x-15)(12x-21)=0

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Solution for x(12x-15)(12x-21)=0 equation: 


Simplifying
x(12x + -15)(12x + -21) = 0

Reorder the terms:
x(-15 + 12x)(12x + -21) = 0

Reorder the terms:
x(-15 + 12x)(-21 + 12x) = 0

Multiply (-15 + 12x) * (-21 + 12x)
x(-15(-21 + 12x) + 12x * (-21 + 12x)) = 0
x((-21 * -15 + 12x * -15) + 12x * (-21 + 12x)) = 0
x((315 + -180x) + 12x * (-21 + 12x)) = 0
x(315 + -180x + (-21 * 12x + 12x * 12x)) = 0
x(315 + -180x + (-252x + 144x2)) = 0

Combine like terms: -180x + -252x = -432x
x(315 + -432x + 144x2) = 0
(315 * x + -432x * x + 144x2 * x) = 0
(315x + -432x2 + 144x3) = 0

Solving
315x + -432x2 + 144x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(35 + -48x + 16x2) = 0

Factor a trinomial.
9x((5 + -4x)(7 + -4x)) = 0

Ignore the factor 9.

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 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 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 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25

Subproblem 3
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {0, 1.25, 1.75}

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