-12x^2(3x-2)(4x-1)=0

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Solution for -12x^2(3x-2)(4x-1)=0 equation: 


Simplifying
-12x2(3x + -2)(4x + -1) = 0

Reorder the terms:
-12x2(-2 + 3x)(4x + -1) = 0

Reorder the terms:
-12x2(-2 + 3x)(-1 + 4x) = 0

Multiply (-2 + 3x) * (-1 + 4x)
-12x2(-2(-1 + 4x) + 3x * (-1 + 4x)) = 0
-12x2((-1 * -2 + 4x * -2) + 3x * (-1 + 4x)) = 0
-12x2((2 + -8x) + 3x * (-1 + 4x)) = 0
-12x2(2 + -8x + (-1 * 3x + 4x * 3x)) = 0
-12x2(2 + -8x + (-3x + 12x2)) = 0

Combine like terms: -8x + -3x = -11x
-12x2(2 + -11x + 12x2) = 0
(2 * -12x2 + -11x * -12x2 + 12x2 * -12x2) = 0
(-24x2 + 132x3 + -144x4) = 0

Solving
-24x2 + 132x3 + -144x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x2'.
12x2(-2 + 11x + -12x2) = 0

Factor a trinomial.
12x2((-2 + 3x)(1 + -4x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
-2 + 3x = 0

Solving
-2 + 3x = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3x = 0 + 2
3x = 0 + 2

Combine like terms: 0 + 2 = 2
3x = 2

Divide each side by '3'.
x = 0.6666666667

Simplifying
x = 0.6666666667

Subproblem 3
Set the factor '(1 + -4x)' equal to zero and attempt to solve:

Simplifying
1 + -4x = 0

Solving
1 + -4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25
Solution
x = {0, 0.6666666667, 0.25}

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