t*(t+6)=0

Solution for t*(t+6)=0 equation:

Simplifying
t(t + 6) = 0

Reorder the terms:
t(6 + t) = 0
(6 * t + t * t) = 0
(6t + t2) = 0

Solving
6t + t2 = 0

Solving for variable 't'.

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

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 '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Solution
t = {0, -6}