3x^2(x+1)-x(x^2-1)=0

Solution for 3x^2(x+1)-x(x^2-1)=0 equation:

Simplifying
3x2(x + 1) + -1x(x2 + -1) = 0

Reorder the terms:
3x2(1 + x) + -1x(x2 + -1) = 0
(1 * 3x2 + x * 3x2) + -1x(x2 + -1) = 0
(3x2 + 3x3) + -1x(x2 + -1) = 0

Reorder the terms:
3x2 + 3x3 + -1x(-1 + x2) = 0
3x2 + 3x3 + (-1 * -1x + x2 * -1x) = 0
3x2 + 3x3 + (1x + -1x3) = 0

Reorder the terms:
1x + 3x2 + 3x3 + -1x3 = 0

Combine like terms: 3x3 + -1x3 = 2x3
1x + 3x2 + 2x3 = 0

Solving
1x + 3x2 + 2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + 3x + 2x2) = 0

Factor a trinomial.
x((1 + 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 + 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
Subproblem 3
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, -1, -0.5}