x(12x+16)(4x-1)=0

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Solution for x(12x+16)(4x-1)=0 equation: 


Simplifying
x(12x + 16)(4x + -1) = 0

Reorder the terms:
x(16 + 12x)(4x + -1) = 0

Reorder the terms:
x(16 + 12x)(-1 + 4x) = 0

Multiply (16 + 12x) * (-1 + 4x)
x(16(-1 + 4x) + 12x * (-1 + 4x)) = 0
x((-1 * 16 + 4x * 16) + 12x * (-1 + 4x)) = 0
x((-16 + 64x) + 12x * (-1 + 4x)) = 0
x(-16 + 64x + (-1 * 12x + 4x * 12x)) = 0
x(-16 + 64x + (-12x + 48x2)) = 0

Combine like terms: 64x + -12x = 52x
x(-16 + 52x + 48x2) = 0
(-16 * x + 52x * x + 48x2 * x) = 0
(-16x + 52x2 + 48x3) = 0

Solving
-16x + 52x2 + 48x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-4 + 13x + 12x2) = 0

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

Ignore the factor 4.

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 '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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, -1.333333333, 0.25}

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