6t(2t-9)=0

Solution for 6t(2t-9)=0 equation:

Simplifying
6t(2t + -9) = 0

Reorder the terms:
6t(-9 + 2t) = 0
(-9 * 6t + 2t * 6t) = 0
(-54t + 12t2) = 0

Solving
-54t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t'.
6t(-9 + 2t) = 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 '(-9 + 2t)' equal to zero and attempt to solve:

Simplifying
-9 + 2t = 0

Solving
-9 + 2t = 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 + 2t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2t = 0 + 9
2t = 0 + 9

Combine like terms: 0 + 9 = 9
2t = 9

Divide each side by '2'.
t = 4.5

Simplifying
t = 4.5
Solution
t = {0, 4.5}