-16t^2-25t+114=0

Solution for -16t^2-25t+114=0 equation:

Simplifying
-16t2 + -25t + 114 = 0

Reorder the terms:
114 + -25t + -16t2 = 0

Solving
114 + -25t + -16t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + -1t)(57 + 16t) = 0

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 '(57 + 16t)' equal to zero and attempt to solve:

Simplifying
57 + 16t = 0

Solving
57 + 16t = 0

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

Add '-57' to each side of the equation.
57 + -57 + 16t = 0 + -57

Combine like terms: 57 + -57 = 0
0 + 16t = 0 + -57
16t = 0 + -57

Combine like terms: 0 + -57 = -57
16t = -57

Divide each side by '16'.
t = -3.5625

Simplifying
t = -3.5625
Solution
t = {2, -3.5625}