12t^2-42t+30=0

Solution for 12t^2-42t+30=0 equation:

Simplifying
12t2 + -42t + 30 = 0

Reorder the terms:
30 + -42t + 12t2 = 0

Solving
30 + -42t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -7t + 2t2) = 0

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

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

Simplifying
1 + -1t = 0

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

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

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

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

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

Simplifying
5 + -2t = 0

Solving
5 + -2t = 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 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {1, 2.5}