3t^2+27t=0

Solution for 3t^2+27t=0 equation:

Simplifying
3t2 + 27t = 0

Reorder the terms:
27t + 3t2 = 0

Solving
27t + 3t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3t'.
3t(9 + 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 '(9 + t)' equal to zero and attempt to solve:

Simplifying
9 + t = 0

Solving
9 + t = 0

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

Add '-9' to each side of the equation.
9 + -9 + t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + t = 0 + -9
t = 0 + -9

Combine like terms: 0 + -9 = -9
t = -9

Simplifying
t = -9
Solution
t = {0, -9}