0=3x^4+12x^3-12x^2-48x

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Solution for 0=3x^4+12x^3-12x^2-48x equation: 


Simplifying
0 = 3x4 + 12x3 + -12x2 + -48x

Reorder the terms:
0 = -48x + -12x2 + 12x3 + 3x4

Solving
0 = -48x + -12x2 + 12x3 + 3x4

Solving for variable 'x'.
Remove the zero:
48x + 12x2 + -12x3 + -3x4 = -48x + -12x2 + 12x3 + 3x4 + 48x + 12x2 + -12x3 + -3x4

Reorder the terms:
48x + 12x2 + -12x3 + -3x4 = -48x + 48x + -12x2 + 12x2 + 12x3 + -12x3 + 3x4 + -3x4

Combine like terms: -48x + 48x = 0
48x + 12x2 + -12x3 + -3x4 = 0 + -12x2 + 12x2 + 12x3 + -12x3 + 3x4 + -3x4
48x + 12x2 + -12x3 + -3x4 = -12x2 + 12x2 + 12x3 + -12x3 + 3x4 + -3x4

Combine like terms: -12x2 + 12x2 = 0
48x + 12x2 + -12x3 + -3x4 = 0 + 12x3 + -12x3 + 3x4 + -3x4
48x + 12x2 + -12x3 + -3x4 = 12x3 + -12x3 + 3x4 + -3x4

Combine like terms: 12x3 + -12x3 = 0
48x + 12x2 + -12x3 + -3x4 = 0 + 3x4 + -3x4
48x + 12x2 + -12x3 + -3x4 = 3x4 + -3x4

Combine like terms: 3x4 + -3x4 = 0
48x + 12x2 + -12x3 + -3x4 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(16 + 4x + -4x2 + -1x3) = 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 '(16 + 4x + -4x2 + -1x3)' equal to zero and attempt to solve:

Simplifying
16 + 4x + -4x2 + -1x3 = 0

Solving
16 + 4x + -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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