-8(2t+5)(6-t)=0

Solution for -8(2t+5)(6-t)=0 equation:

Simplifying
-8(2t + 5)(6 + -1t) = 0

Reorder the terms:
-8(5 + 2t)(6 + -1t) = 0

Multiply (5 + 2t) * (6 + -1t)
-8(5(6 + -1t) + 2t * (6 + -1t)) = 0
-8((6 * 5 + -1t * 5) + 2t * (6 + -1t)) = 0
-8((30 + -5t) + 2t * (6 + -1t)) = 0
-8(30 + -5t + (6 * 2t + -1t * 2t)) = 0
-8(30 + -5t + (12t + -2t2)) = 0

Combine like terms: -5t + 12t = 7t
-8(30 + 7t + -2t2) = 0
(30 * -8 + 7t * -8 + -2t2 * -8) = 0
(-240 + -56t + 16t2) = 0

Solving
-240 + -56t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-30 + -7t + 2t2) = 0

Factor a trinomial.
8((-5 + -2t)(6 + -1t)) = 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 '(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}