6t^2+31t-30=0

Solution for 6t^2+31t-30=0 equation:

Simplifying
6t2 + 31t + -30 = 0

Reorder the terms:
-30 + 31t + 6t2 = 0

Solving
-30 + 31t + 6t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -6t)' equal to zero and attempt to solve:

Simplifying
5 + -6t = 0

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

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

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

Divide each side by '-6'.
t = 0.8333333333

Simplifying
t = 0.8333333333
Solution
t = {-6, 0.8333333333}