(-4t^3)+(12t^2)=0

Solution for (-4t^3)+(12t^2)=0 equation:

Simplifying
(-4t3) + (12t2) = 0

Reorder the terms:
(12t2) + (-4t3) = 0

Solving
(12t2) + (-4t3) = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4t2'.
4t2(3 + (-1t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 't2' equal to zero and attempt to solve:

Simplifying
t2 = 0

Solving
t2 = 0

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

Simplifying
t2 = 0

Take the square root of each side:
t = {0}
Subproblem 2
Set the factor '(3 + (-1t))' equal to zero and attempt to solve:

Simplifying
3 + (-1t) = 0

Solving
3 + (-1t) = 0

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

Add '-3' to each side of the equation.
3 + -3 + (-1t) = 0 + -3

Combine like terms: 3 + -3 = 0
0 + (-1t) = 0 + -3
(-1t) = 0 + -3

Combine like terms: 0 + -3 = -3
(-1t) = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {0, 3}