(t+4)(t+25)=0

Solution for (t+4)(t+25)=0 equation:

Simplifying
(t + 4)(t + 25) = 0

Reorder the terms:
(4 + t)(t + 25) = 0

Reorder the terms:
(4 + t)(25 + t) = 0

Multiply (4 + t) * (25 + t)
(4(25 + t) + t(25 + t)) = 0
((25 * 4 + t * 4) + t(25 + t)) = 0
((100 + 4t) + t(25 + t)) = 0
(100 + 4t + (25 * t + t * t)) = 0
(100 + 4t + (25t + t2)) = 0

Combine like terms: 4t + 25t = 29t
(100 + 29t + t2) = 0

Solving
100 + 29t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(25 + t)' equal to zero and attempt to solve:

Simplifying
25 + t = 0

Solving
25 + t = 0

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

Add '-25' to each side of the equation.
25 + -25 + t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + t = 0 + -25
t = 0 + -25

Combine like terms: 0 + -25 = -25
t = -25

Simplifying
t = -25
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 = {-25, -4}