2(-8t^2+2t+15)=0

Solution for 2(-8t^2+2t+15)=0 equation:

Simplifying
2(-8t2 + 2t + 15) = 0

Reorder the terms:
2(15 + 2t + -8t2) = 0
(15 * 2 + 2t * 2 + -8t2 * 2) = 0
(30 + 4t + -16t2) = 0

Solving
30 + 4t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 2t + -8t2) = 0

Factor a trinomial.
2((3 + -2t)(5 + 4t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Solution
t = {1.5, -1.25}