3t^2+12t=0

Solution for 3t^2+12t=0 equation:

Simplifying
3t2 + 12t = 0

Reorder the terms:
12t + 3t2 = 0

Solving
12t + 3t2 = 0

Solving for variable 't'.

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

Ignore the factor 3.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

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

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

Simplifying
t = -4
Solution
t = {0, -4}