4x^3+12x^2=0

Solution for 4x^3+12x^2=0 equation:

Simplifying
4x3 + 12x2 = 0

Reorder the terms:
12x2 + 4x3 = 0

Solving
12x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x2'.
4x2(3 + x) = 0

Ignore the factor 4.
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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {0, -3}