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

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

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

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

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

Multiply (-4 + t) * (16 + t)
(-4(16 + t) + t(16 + t)) = 0
((16 * -4 + t * -4) + t(16 + t)) = 0
((-64 + -4t) + t(16 + t)) = 0
(-64 + -4t + (16 * t + t * t)) = 0
(-64 + -4t + (16t + t2)) = 0

Combine like terms: -4t + 16t = 12t
(-64 + 12t + t2) = 0

Solving
-64 + 12t + t2 = 0

Solving for variable 't'.

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

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

Simplifying
-16 + -1t = 0

Solving
-16 + -1t = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1t = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1t = 0 + 16
-1t = 0 + 16

Combine like terms: 0 + 16 = 16
-1t = 16

Divide each side by '-1'.
t = -16

Simplifying
t = -16
Subproblem 2
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
Solution
t = {-16, 4}