-16(t-10)(t+4)=0

Solution for -16(t-10)(t+4)=0 equation:

Simplifying
-16(t + -10)(t + 4) = 0

Reorder the terms:
-16(-10 + t)(t + 4) = 0

Reorder the terms:
-16(-10 + t)(4 + t) = 0

Multiply (-10 + t) * (4 + t)
-16(-10(4 + t) + t(4 + t)) = 0
-16((4 * -10 + t * -10) + t(4 + t)) = 0
-16((-40 + -10t) + t(4 + t)) = 0
-16(-40 + -10t + (4 * t + t * t)) = 0
-16(-40 + -10t + (4t + t2)) = 0

Combine like terms: -10t + 4t = -6t
-16(-40 + -6t + t2) = 0
(-40 * -16 + -6t * -16 + t2 * -16) = 0
(640 + 96t + -16t2) = 0

Solving
640 + 96t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(40 + 6t + -1t2) = 0

Factor a trinomial.
16((10 + -1t)(4 + t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve:

Simplifying
10 + -1t = 0

Solving
10 + -1t = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1t = 0 + -10
-1t = 0 + -10

Combine like terms: 0 + -10 = -10
-1t = -10

Divide each side by '-1'.
t = 10

Simplifying
t = 10
Subproblem 2
Set the factor '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 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 + t = 0 + -4

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

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

Simplifying
t = -4
Solution
t = {10, -4}