0=4x^4-16x^3+8x^2+12x

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Solution for 0=4x^4-16x^3+8x^2+12x equation: 


Simplifying
0 = 4x4 + -16x3 + 8x2 + 12x

Reorder the terms:
0 = 12x + 8x2 + -16x3 + 4x4

Solving
0 = 12x + 8x2 + -16x3 + 4x4

Solving for variable 'x'.
Remove the zero:
-12x + -8x2 + 16x3 + -4x4 = 12x + 8x2 + -16x3 + 4x4 + -12x + -8x2 + 16x3 + -4x4

Reorder the terms:
-12x + -8x2 + 16x3 + -4x4 = 12x + -12x + 8x2 + -8x2 + -16x3 + 16x3 + 4x4 + -4x4

Combine like terms: 12x + -12x = 0
-12x + -8x2 + 16x3 + -4x4 = 0 + 8x2 + -8x2 + -16x3 + 16x3 + 4x4 + -4x4
-12x + -8x2 + 16x3 + -4x4 = 8x2 + -8x2 + -16x3 + 16x3 + 4x4 + -4x4

Combine like terms: 8x2 + -8x2 = 0
-12x + -8x2 + 16x3 + -4x4 = 0 + -16x3 + 16x3 + 4x4 + -4x4
-12x + -8x2 + 16x3 + -4x4 = -16x3 + 16x3 + 4x4 + -4x4

Combine like terms: -16x3 + 16x3 = 0
-12x + -8x2 + 16x3 + -4x4 = 0 + 4x4 + -4x4
-12x + -8x2 + 16x3 + -4x4 = 4x4 + -4x4

Combine like terms: 4x4 + -4x4 = 0
-12x + -8x2 + 16x3 + -4x4 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-3 + -2x + 4x2 + -1x3) = 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 '(-3 + -2x + 4x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
-3 + -2x + 4x2 + -1x3 = 0

Solving
-3 + -2x + 4x2 + -1x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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