6t^2-42t+60=0

Solution for 6t^2-42t+60=0 equation:

Simplifying
6t2 + -42t + 60 = 0

Reorder the terms:
60 + -42t + 6t2 = 0

Solving
60 + -42t + 6t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + -7t + t2) = 0

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

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
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 = {2, 5}