4x^4=8x^3-32x^2

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Solution for 4x^4=8x^3-32x^2 equation: 


Simplifying
4x4 = 8x3 + -32x2

Reorder the terms:
4x4 = -32x2 + 8x3

Solving
4x4 = -32x2 + 8x3

Solving for variable 'x'.

Reorder the terms:
32x2 + -8x3 + 4x4 = -32x2 + 8x3 + 32x2 + -8x3

Reorder the terms:
32x2 + -8x3 + 4x4 = -32x2 + 32x2 + 8x3 + -8x3

Combine like terms: -32x2 + 32x2 = 0
32x2 + -8x3 + 4x4 = 0 + 8x3 + -8x3
32x2 + -8x3 + 4x4 = 8x3 + -8x3

Combine like terms: 8x3 + -8x3 = 0
32x2 + -8x3 + 4x4 = 0

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(8 + -2x + x2) = 0

Ignore the factor 4.

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 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
8 + -2x + x2 = 0

Solving
8 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + -2x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + -2x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -2x + x2 = 0 + -8
-2x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
-2x + x2 = -8

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -8 + 1

Reorder the terms:
1 + -2x + x2 = -8 + 1

Combine like terms: -8 + 1 = -7
1 + -2x + x2 = -7

Factor a perfect square on the left side:
(x + -1)(x + -1) = -7

Can't calculate square root of the right side.

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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