x^3+2x^2+x-3=x-3

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

Simplifying
x3 + 2x2 + x + -3 = x + -3

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

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

Add '3' to each side of the equation.
-3 + x + 2x2 + 3 + x3 = -3 + 3 + x

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

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

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

Add '-1x' to each side of the equation.
x + 2x2 + -1x + x3 = x + -1x

Reorder the terms:
x + -1x + 2x2 + x3 = x + -1x

Combine like terms: x + -1x = 0
0 + 2x2 + x3 = x + -1x
2x2 + x3 = x + -1x

Combine like terms: x + -1x = 0
2x2 + x3 = 0

Solving
2x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {0, -2}