8(-2t^2+t+10)=0

Solution for 8(-2t^2+t+10)=0 equation:

Simplifying
8(-2t2 + t + 10) = 0

Reorder the terms:
8(10 + t + -2t2) = 0
(10 * 8 + t * 8 + -2t2 * 8) = 0
(80 + 8t + -16t2) = 0

Solving
80 + 8t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(10 + t + -2t2) = 0

Factor a trinomial.
8((5 + -2t)(2 + t)) = 0

Ignore the factor 8.
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 '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 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 + t = 0 + -2

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

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

Simplifying
t = -2
Solution
t = {2.5, -2}