4x=x^3-3x^2

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

Simplifying
4x = x3 + -3x2

Reorder the terms:
4x = -3x2 + x3

Solving
4x = -3x2 + x3

Solving for variable 'x'.

Reorder the terms:
4x + 3x2 + -1x3 = -3x2 + 3x2 + x3 + -1x3

Combine like terms: -3x2 + 3x2 = 0
4x + 3x2 + -1x3 = 0 + x3 + -1x3
4x + 3x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
4x + 3x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(4 + 3x + -1x2) = 0

Factor a trinomial.
x((4 + -1x)(1 + x)) = 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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 3
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {0, 4, -1}