-32(t-8)(t+2)=

Solution for -32(t-8)(t+2)= equation:

Simplifying
-32(t + -8)(t + 2) = 0

Reorder the terms:
-32(-8 + t)(t + 2) = 0

Reorder the terms:
-32(-8 + t)(2 + t) = 0

Multiply (-8 + t) * (2 + t)
-32(-8(2 + t) + t(2 + t)) = 0
-32((2 * -8 + t * -8) + t(2 + t)) = 0
-32((-16 + -8t) + t(2 + t)) = 0
-32(-16 + -8t + (2 * t + t * t)) = 0
-32(-16 + -8t + (2t + t2)) = 0

Combine like terms: -8t + 2t = -6t
-32(-16 + -6t + t2) = 0
(-16 * -32 + -6t * -32 + t2 * -32) = 0
(512 + 192t + -32t2) = 0

Solving
512 + 192t + -32t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '32'.
32(16 + 6t + -1t2) = 0

Factor a trinomial.
32((8 + -1t)(2 + t)) = 0

Ignore the factor 32.
Subproblem 1
Set the factor '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
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 = {8, -2}