t^2+12t+15=-5

Solution for t^2+12t+15=-5 equation:

Simplifying
t2 + 12t + 15 = -5

Reorder the terms:
15 + 12t + t2 = -5

Solving
15 + 12t + t2 = -5

Solving for variable 't'.

Reorder the terms:
15 + 5 + 12t + t2 = -5 + 5

Combine like terms: 15 + 5 = 20
20 + 12t + t2 = -5 + 5

Combine like terms: -5 + 5 = 0
20 + 12t + t2 = 0

Factor a trinomial.
(10 + t)(2 + t) = 0

Subproblem 1
Set the factor '(10 + t)' equal to zero and attempt to solve:

Simplifying
10 + t = 0

Solving
10 + t = 0

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

Add '-10' to each side of the equation.
10 + -10 + t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + t = 0 + -10
t = 0 + -10

Combine like terms: 0 + -10 = -10
t = -10

Simplifying
t = -10
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Solution
t = {-10, -2}