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

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

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

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

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

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

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

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

Solving
2x2 = 1x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
-1 + 2x = 0

Solving
-1 + 2x = 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 + 2x = 0 + 1

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

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

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0, 0.5}