x^3=4x^2-5x

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Solution for x^3=4x^2-5x equation: 


Simplifying
x3 = 4x2 + -5x

Reorder the terms:
x3 = -5x + 4x2

Solving
x3 = -5x + 4x2

Solving for variable 'x'.

Reorder the terms:
5x + -4x2 + x3 = -5x + 4x2 + 5x + -4x2

Reorder the terms:
5x + -4x2 + x3 = -5x + 5x + 4x2 + -4x2

Combine like terms: -5x + 5x = 0
5x + -4x2 + x3 = 0 + 4x2 + -4x2
5x + -4x2 + x3 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
5x + -4x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -4x + x2) = 0


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 '(5 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -4x + x2 = 0

Solving
5 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -4x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -4x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x + x2 = 0 + -5
-4x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-4x + x2 = -5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -5 + 4

Reorder the terms:
4 + -4x + x2 = -5 + 4

Combine like terms: -5 + 4 = -1
4 + -4x + x2 = -1

Factor a perfect square on the left side:
(x + -2)(x + -2) = -1

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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