2x^4+12x^3=32x^2

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Solution for 2x^4+12x^3=32x^2 equation: 


Simplifying
2x4 + 12x3 = 32x2

Reorder the terms:
12x3 + 2x4 = 32x2

Solving
12x3 + 2x4 = 32x2

Solving for variable 'x'.

Reorder the terms:
-32x2 + 12x3 + 2x4 = 32x2 + -32x2

Combine like terms: 32x2 + -32x2 = 0
-32x2 + 12x3 + 2x4 = 0

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-16 + 6x + x2) = 0

Factor a trinomial.
2x2((-8 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

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 '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, -8, 2}

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