x+(x-1)(x^2+2x)=x(x^2+2x)

Solution for x+(x-1)(x^2+2x)=x(x^2+2x) equation:

Simplifying
x + (x + -1)(x2 + 2x) = x(x2 + 2x)

Reorder the terms:
x + (-1 + x)(x2 + 2x) = x(x2 + 2x)

Reorder the terms:
x + (-1 + x)(2x + x2) = x(x2 + 2x)

Multiply (-1 + x) * (2x + x2)
x + (-1(2x + x2) + x(2x + x2)) = x(x2 + 2x)
x + ((2x * -1 + x2 * -1) + x(2x + x2)) = x(x2 + 2x)
x + ((-2x + -1x2) + x(2x + x2)) = x(x2 + 2x)
x + (-2x + -1x2 + (2x * x + x2 * x)) = x(x2 + 2x)
x + (-2x + -1x2 + (2x2 + x3)) = x(x2 + 2x)

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

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

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

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

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

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

Solving
-1x + 1x2 = 2x2

Solving for variable 'x'.

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

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

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

Ignore the factor -1.
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 + 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, -1}