(t+4)(t+64)=0

Solution for (t+4)(t+64)=0 equation:

Simplifying
(t + 4)(t + 64) = 0

Reorder the terms:
(4 + t)(t + 64) = 0

Reorder the terms:
(4 + t)(64 + t) = 0

Multiply (4 + t) * (64 + t)
(4(64 + t) + t(64 + t)) = 0
((64 * 4 + t * 4) + t(64 + t)) = 0
((256 + 4t) + t(64 + t)) = 0
(256 + 4t + (64 * t + t * t)) = 0
(256 + 4t + (64t + t2)) = 0

Combine like terms: 4t + 64t = 68t
(256 + 68t + t2) = 0

Solving
256 + 68t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(64 + t)(4 + t) = 0

Subproblem 1
Set the factor '(64 + t)' equal to zero and attempt to solve:

Simplifying
64 + t = 0

Solving
64 + t = 0

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

Add '-64' to each side of the equation.
64 + -64 + t = 0 + -64

Combine like terms: 64 + -64 = 0
0 + t = 0 + -64
t = 0 + -64

Combine like terms: 0 + -64 = -64
t = -64

Simplifying
t = -64
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 = {-64, -4}