6t(5t-6)(6t-1)=0

Solution for 6t(5t-6)(6t-1)=0 equation:

Simplifying
6t(5t + -6)(6t + -1) = 0

Reorder the terms:
6t(-6 + 5t)(6t + -1) = 0

Reorder the terms:
6t(-6 + 5t)(-1 + 6t) = 0

Multiply (-6 + 5t) * (-1 + 6t)
6t(-6(-1 + 6t) + 5t * (-1 + 6t)) = 0
6t((-1 * -6 + 6t * -6) + 5t * (-1 + 6t)) = 0
6t((6 + -36t) + 5t * (-1 + 6t)) = 0
6t(6 + -36t + (-1 * 5t + 6t * 5t)) = 0
6t(6 + -36t + (-5t + 30t2)) = 0

Combine like terms: -36t + -5t = -41t
6t(6 + -41t + 30t2) = 0
(6 * 6t + -41t * 6t + 30t2 * 6t) = 0
(36t + -246t2 + 180t3) = 0

Solving
36t + -246t2 + 180t3 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6t'.
6t(6 + -41t + 30t2) = 0

Factor a trinomial.
6t((1 + -6t)(6 + -5t)) = 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 '(1 + -6t)' equal to zero and attempt to solve:

Simplifying
1 + -6t = 0

Solving
1 + -6t = 0

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

Add '-1' to each side of the equation.
1 + -1 + -6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6t = 0 + -1
-6t = 0 + -1

Combine like terms: 0 + -1 = -1
-6t = -1

Divide each side by '-6'.
t = 0.1666666667

Simplifying
t = 0.1666666667
Subproblem 3
Set the factor '(6 + -5t)' equal to zero and attempt to solve:

Simplifying
6 + -5t = 0

Solving
6 + -5t = 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 + -5t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5t = 0 + -6
-5t = 0 + -6

Combine like terms: 0 + -6 = -6
-5t = -6

Divide each side by '-5'.
t = 1.2

Simplifying
t = 1.2
Solution
t = {0, 0.1666666667, 1.2}