(x^4)=(x^3)-(4x^2)

Solution for (x^4)=(x^3)-(4x^2) equation:

Simplifying
(x4) = (x3) + -1(4x2)
x4 = (x3) + -1(4x2)
x4 = x3 + -1(4x2)

Remove parenthesis around (4x2)
x4 = x3 + -1 * 4x2

Multiply -1 * 4
x4 = x3 + -4x2

Reorder the terms:
x4 = -4x2 + x3

Solving
x4 = -4x2 + x3

Solving for variable 'x'.

Reorder the terms:
4x2 + -1x3 + x4 = -4x2 + x3 + 4x2 + -1x3

Reorder the terms:
4x2 + -1x3 + x4 = -4x2 + 4x2 + x3 + -1x3

Combine like terms: -4x2 + 4x2 = 0
4x2 + -1x3 + x4 = 0 + x3 + -1x3
4x2 + -1x3 + x4 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
4x2 + -1x3 + x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(4 + -1x + x2) = 0

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 '(4 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
4 + -1x + x2 = 0

Solving
4 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -1x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -1x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x + x2 = 0 + -4
-1x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1x + x2 = -4

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -4 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -1x + x2 = -3.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -3.75

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}