x^3=2x^2+3x

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Solution for x^3=2x^2+3x equation: 


Simplifying
x3 = 2x2 + 3x

Reorder the terms:
x3 = 3x + 2x2

Solving
x3 = 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
-3x + -2x2 + x3 = 3x + 2x2 + -3x + -2x2

Reorder the terms:
-3x + -2x2 + x3 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
-3x + -2x2 + x3 = 0 + 2x2 + -2x2
-3x + -2x2 + x3 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-3x + -2x2 + x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-3 + -2x + x2) = 0

Factor a trinomial.
x((-1 + -1x)(3 + -1x)) = 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 '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -1, 3}

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