4t^2+12t=0

Solution for 4t^2+12t=0 equation:

Simplifying
4t2 + 12t = 0

Reorder the terms:
12t + 4t2 = 0

Solving
12t + 4t2 = 0

Solving for variable 't'.

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

Ignore the factor 4.
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 '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 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 + t = 0 + -3

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

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

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