2t(t-1)=60

Solution for 2t(t-1)=60 equation:

Simplifying
2t(t + -1) = 60

Reorder the terms:
2t(-1 + t) = 60
(-1 * 2t + t * 2t) = 60
(-2t + 2t2) = 60

Solving
-2t + 2t2 = 60

Solving for variable 't'.

Reorder the terms:
-60 + -2t + 2t2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -2t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + -1t + t2) = 0

Factor a trinomial.
2((-5 + -1t)(6 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 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 + -1t = 0 + -6

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

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

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {-5, 6}