3x(x^3+7x^2)(-16x+12)=0

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Solution for 3x(x^3+7x^2)(-16x+12)=0 equation: 


Simplifying
3x(x3 + 7x2)(-16x + 12) = 0

Reorder the terms:
3x(7x2 + x3)(-16x + 12) = 0

Reorder the terms:
3x(7x2 + x3)(12 + -16x) = 0

Multiply (7x2 + x3) * (12 + -16x)
3x(7x2 * (12 + -16x) + x3(12 + -16x)) = 0
3x((12 * 7x2 + -16x * 7x2) + x3(12 + -16x)) = 0
3x((84x2 + -112x3) + x3(12 + -16x)) = 0
3x(84x2 + -112x3 + (12 * x3 + -16x * x3)) = 0
3x(84x2 + -112x3 + (12x3 + -16x4)) = 0

Combine like terms: -112x3 + 12x3 = -100x3
3x(84x2 + -100x3 + -16x4) = 0
(84x2 * 3x + -100x3 * 3x + -16x4 * 3x) = 0
(252x3 + -300x4 + -48x5) = 0

Solving
252x3 + -300x4 + -48x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x3'.
12x3(21 + -25x + -4x2) = 0

Factor a trinomial.
12x3((3 + -4x)(7 + x)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 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 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75

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

Simplifying
7 + x = 0

Solving
7 + x = 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 + x = 0 + -7

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

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

Simplifying
x = -7
Solution
x = {0.75, -7}

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