2t^2-7t-30=0

Solution for 2t^2-7t-30=0 equation:

Simplifying
2t2 + -7t + -30 = 0

Reorder the terms:
-30 + -7t + 2t2 = 0

Solving
-30 + -7t + 2t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
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 = {-2.5, 6}