x^3-x^2=-42x

Solution for x^3-x^2=-42x equation:

Simplifying
x3 + -1x2 = -42x

Reorder the terms:
-1x2 + x3 = -42x

Solving
-1x2 + x3 = -42x

Solving for variable 'x'.

Reorder the terms:
42x + -1x2 + x3 = -42x + 42x

Combine like terms: -42x + 42x = 0
42x + -1x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(42 + -1x + 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 '(42 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
42 + -1x + x2 = 0

Solving
42 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-42' to each side of the equation.
42 + -1x + -42 + x2 = 0 + -42

Reorder the terms:
42 + -42 + -1x + x2 = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x + x2 = 0 + -42
-1x + x2 = 0 + -42

Combine like terms: 0 + -42 = -42
-1x + x2 = -42

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 = -42 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -42 + 0.25

Combine like terms: -42 + 0.25 = -41.75
0.25 + -1x + x2 = -41.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -41.75

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}