3t(t-1)=60

Solution for 3t(t-1)=60 equation:

Simplifying
3t(t + -1) = 60

Reorder the terms:
3t(-1 + t) = 60
(-1 * 3t + t * 3t) = 60
(-3t + 3t2) = 60

Solving
-3t + 3t2 = 60

Solving for variable 't'.

Reorder the terms:
-60 + -3t + 3t2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -3t + 3t2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -1t + t2) = 0

Factor a trinomial.
3((-4 + -1t)(5 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -1t)' equal to zero and attempt to solve:

Simplifying
-4 + -1t = 0

Solving
-4 + -1t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1t = 0 + 4
-1t = 0 + 4

Combine like terms: 0 + 4 = 4
-1t = 4

Divide each side by '-1'.
t = -4

Simplifying
t = -4
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-4, 5}