0=t^2+8t+15

Solution for 0=t^2+8t+15 equation:

Simplifying
0 = t2 + 8t + 15

Reorder the terms:
0 = 15 + 8t + t2

Solving
0 = 15 + 8t + t2

Solving for variable 't'.

Combine like terms: 0 + -15 = -15
-15 + -8t + -1t2 = 15 + 8t + t2 + -15 + -8t + -1t2

Reorder the terms:
-15 + -8t + -1t2 = 15 + -15 + 8t + -8t + t2 + -1t2

Combine like terms: 15 + -15 = 0
-15 + -8t + -1t2 = 0 + 8t + -8t + t2 + -1t2
-15 + -8t + -1t2 = 8t + -8t + t2 + -1t2

Combine like terms: 8t + -8t = 0
-15 + -8t + -1t2 = 0 + t2 + -1t2
-15 + -8t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-15 + -8t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 8t + t2) = 0

Factor a trinomial.
-1((5 + t)(3 + t)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve:

Simplifying
5 + t = 0

Solving
5 + t = 0

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

Add '-5' to each side of the equation.
5 + -5 + t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + t = 0 + -5
t = 0 + -5

Combine like terms: 0 + -5 = -5
t = -5

Simplifying
t = -5
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 = {-5, -3}