x(12x-5)(12x-21)=0

Solution for x(12x-5)(12x-21)=0 equation:

Simplifying
x(12x + -5)(12x + -21) = 0

Reorder the terms:
x(-5 + 12x)(12x + -21) = 0

Reorder the terms:
x(-5 + 12x)(-21 + 12x) = 0

Multiply (-5 + 12x) * (-21 + 12x)
x(-5(-21 + 12x) + 12x * (-21 + 12x)) = 0
x((-21 * -5 + 12x * -5) + 12x * (-21 + 12x)) = 0
x((105 + -60x) + 12x * (-21 + 12x)) = 0
x(105 + -60x + (-21 * 12x + 12x * 12x)) = 0
x(105 + -60x + (-252x + 144x2)) = 0

Combine like terms: -60x + -252x = -312x
x(105 + -312x + 144x2) = 0
(105 * x + -312x * x + 144x2 * x) = 0
(105x + -312x2 + 144x3) = 0

Solving
105x + -312x2 + 144x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(35 + -104x + 48x2) = 0

Factor a trinomial.
3x((5 + -12x)(7 + -4x)) = 0

Ignore the factor 3.
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 + -12x)' equal to zero and attempt to solve:

Simplifying
5 + -12x = 0

Solving
5 + -12x = 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 + -12x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -12x = 0 + -5
-12x = 0 + -5

Combine like terms: 0 + -5 = -5
-12x = -5

Divide each side by '-12'.
x = 0.4166666667

Simplifying
x = 0.4166666667
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, 0.4166666667, 1.75}