(t+3)(t+1)=0

Solution for (t+3)(t+1)=0 equation:

Simplifying
(t + 3)(t + 1) = 0

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

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

Multiply (3 + t) * (1 + t)
(3(1 + t) + t(1 + t)) = 0
((1 * 3 + t * 3) + t(1 + t)) = 0
((3 + 3t) + t(1 + t)) = 0
(3 + 3t + (1 * t + t * t)) = 0
(3 + 3t + (1t + t2)) = 0

Combine like terms: 3t + 1t = 4t
(3 + 4t + t2) = 0

Solving
3 + 4t + t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
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 = {-3, -1}