-5(t-4)(t+2)=0

Solution for -5(t-4)(t+2)=0 equation:

Simplifying
-5(t + -4)(t + 2) = 0

Reorder the terms:
-5(-4 + t)(t + 2) = 0

Reorder the terms:
-5(-4 + t)(2 + t) = 0

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

Combine like terms: -4t + 2t = -2t
-5(-8 + -2t + t2) = 0
(-8 * -5 + -2t * -5 + t2 * -5) = 0
(40 + 10t + -5t2) = 0

Solving
40 + 10t + -5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(8 + 2t + -1t2) = 0

Factor a trinomial.
5((4 + -1t)(2 + t)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
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 = {4, -2}