(t+8)(t+2)=-5

Solution for (t+8)(t+2)=-5 equation:

Simplifying
(t + 8)(t + 2) = -5

Reorder the terms:
(8 + t)(t + 2) = -5

Reorder the terms:
(8 + t)(2 + t) = -5

Multiply (8 + t) * (2 + t)
(8(2 + t) + t(2 + t)) = -5
((2 * 8 + t * 8) + t(2 + t)) = -5
((16 + 8t) + t(2 + t)) = -5
(16 + 8t + (2 * t + t * t)) = -5
(16 + 8t + (2t + t2)) = -5

Combine like terms: 8t + 2t = 10t
(16 + 10t + t2) = -5

Solving
16 + 10t + t2 = -5

Solving for variable 't'.

Reorder the terms:
16 + 5 + 10t + t2 = -5 + 5

Combine like terms: 16 + 5 = 21
21 + 10t + t2 = -5 + 5

Combine like terms: -5 + 5 = 0
21 + 10t + t2 = 0

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

Subproblem 1
Set the factor '(7 + t)' equal to zero and attempt to solve:

Simplifying
7 + t = 0

Solving
7 + t = 0

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

Add '-7' to each side of the equation.
7 + -7 + t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + t = 0 + -7
t = 0 + -7

Combine like terms: 0 + -7 = -7
t = -7

Simplifying
t = -7
Subproblem 2
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
Solution
t = {-7, -3}