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

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

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

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

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

Multiply (-5 + 2t) * (2 + t)
0 = -8(-5(2 + t) + 2t * (2 + t))
0 = -8((2 * -5 + t * -5) + 2t * (2 + t))
0 = -8((-10 + -5t) + 2t * (2 + t))
0 = -8(-10 + -5t + (2 * 2t + t * 2t))
0 = -8(-10 + -5t + (4t + 2t2))

Combine like terms: -5t + 4t = -1t
0 = -8(-10 + -1t + 2t2)
0 = (-10 * -8 + -1t * -8 + 2t2 * -8)
0 = (80 + 8t + -16t2)

Solving
0 = 80 + 8t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -80 = -80
-80 + -8t + 16t2 = 80 + 8t + -16t2 + -80 + -8t + 16t2

Reorder the terms:
-80 + -8t + 16t2 = 80 + -80 + 8t + -8t + -16t2 + 16t2

Combine like terms: 80 + -80 = 0
-80 + -8t + 16t2 = 0 + 8t + -8t + -16t2 + 16t2
-80 + -8t + 16t2 = 8t + -8t + -16t2 + 16t2

Combine like terms: 8t + -8t = 0
-80 + -8t + 16t2 = 0 + -16t2 + 16t2
-80 + -8t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-80 + -8t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-10 + -1t + 2t2) = 0

Factor a trinomial.
8((-2 + -1t)(5 + -2t)) = 0

Ignore the factor 8.
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 '(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
Solution
t = {-2, 2.5}