2x^2(x+1)(x+3)-6x^2=0

Solution for 2x^2(x+1)(x+3)-6x^2=0 equation:

Simplifying
2x2(x + 1)(x + 3) + -6x2 = 0

Reorder the terms:
2x2(1 + x)(x + 3) + -6x2 = 0

Reorder the terms:
2x2(1 + x)(3 + x) + -6x2 = 0

Multiply (1 + x) * (3 + x)
2x2(1(3 + x) + x(3 + x)) + -6x2 = 0
2x2((3 * 1 + x * 1) + x(3 + x)) + -6x2 = 0
2x2((3 + 1x) + x(3 + x)) + -6x2 = 0
2x2(3 + 1x + (3 * x + x * x)) + -6x2 = 0
2x2(3 + 1x + (3x + x2)) + -6x2 = 0

Combine like terms: 1x + 3x = 4x
2x2(3 + 4x + x2) + -6x2 = 0
(3 * 2x2 + 4x * 2x2 + x2 * 2x2) + -6x2 = 0
(6x2 + 8x3 + 2x4) + -6x2 = 0

Reorder the terms:
6x2 + -6x2 + 8x3 + 2x4 = 0

Combine like terms: 6x2 + -6x2 = 0
0 + 8x3 + 2x4 = 0
8x3 + 2x4 = 0

Solving
8x3 + 2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x3'.
2x3(4 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve:

Simplifying
x3 = 0

Solving
x3 = 0

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

Simplifying
x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-4}