(t+4)(t+1)=0

Solution for (t+4)(t+1)=0 equation:

Simplifying
(t + 4)(t + 1) = 0

Reorder the terms:
(4 + t)(t + 1) = 0

Reorder the terms:
(4 + t)(1 + t) = 0

Multiply (4 + t) * (1 + t)
(4(1 + t) + t(1 + t)) = 0
((1 * 4 + t * 4) + t(1 + t)) = 0
((4 + 4t) + t(1 + t)) = 0
(4 + 4t + (1 * t + t * t)) = 0
(4 + 4t + (1t + t2)) = 0

Combine like terms: 4t + 1t = 5t
(4 + 5t + t2) = 0

Solving
4 + 5t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 0

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

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

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

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

Simplifying
t = -1
Solution
t = {-4, -1}