(6x^2)+(4x^3)=0

Solution for (6x^2)+(4x^3)=0 equation:

Simplifying
(6x2) + (4x3) = 0

Solving
(6x2) + (4x3) = 0

Solving for variable 'x'.

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

Ignore the factor 2.
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 + (2x))' equal to zero and attempt to solve:

Simplifying
3 + (2x) = 0

Solving
3 + (2x) = 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 + (2x) = 0 + -3

Combine like terms: 3 + -3 = 0
0 + (2x) = 0 + -3
(2x) = 0 + -3

Combine like terms: 0 + -3 = -3
(2x) = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {0, -1.5}