0=6t(t-3)

Solution for 0=6t(t-3) equation:

Simplifying
0 = 6t(t + -3)

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

Solving
0 = -18t + 6t2

Solving for variable 't'.
Remove the zero:
18t + -6t2 = -18t + 6t2 + 18t + -6t2

Reorder the terms:
18t + -6t2 = -18t + 18t + 6t2 + -6t2

Combine like terms: -18t + 18t = 0
18t + -6t2 = 0 + 6t2 + -6t2
18t + -6t2 = 6t2 + -6t2

Combine like terms: 6t2 + -6t2 = 0
18t + -6t2 = 0

Factor out the Greatest Common Factor (GCF), '6t'.
6t(3 + -1t) = 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 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

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