2t(3t+9)=0

Solution for 2t(3t+9)=0 equation:

Simplifying
2t(3t + 9) = 0

Reorder the terms:
2t(9 + 3t) = 0
(9 * 2t + 3t * 2t) = 0
(18t + 6t2) = 0

Solving
18t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t'.
6t(3 + t) = 0

Ignore the factor 6.
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}