8t^2-16t-90=0

Solution for 8t^2-16t-90=0 equation:

Simplifying
8t2 + -16t + -90 = 0

Reorder the terms:
-90 + -16t + 8t2 = 0

Solving
-90 + -16t + 8t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -8t + 4t2) = 0

Factor a trinomial.
2((-5 + -2t)(9 + -2t)) = 0

Ignore the factor 2.
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 '(9 + -2t)' equal to zero and attempt to solve:

Simplifying
9 + -2t = 0

Solving
9 + -2t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2t = 0 + -9
-2t = 0 + -9

Combine like terms: 0 + -9 = -9
-2t = -9

Divide each side by '-2'.
t = 4.5

Simplifying
t = 4.5
Solution
t = {-2.5, 4.5}