0=t^2+18t+80

Solution for 0=t^2+18t+80 equation:

Simplifying
0 = t2 + 18t + 80

Reorder the terms:
0 = 80 + 18t + t2

Solving
0 = 80 + 18t + t2

Solving for variable 't'.

Combine like terms: 0 + -80 = -80
-80 + -18t + -1t2 = 80 + 18t + t2 + -80 + -18t + -1t2

Reorder the terms:
-80 + -18t + -1t2 = 80 + -80 + 18t + -18t + t2 + -1t2

Combine like terms: 80 + -80 = 0
-80 + -18t + -1t2 = 0 + 18t + -18t + t2 + -1t2
-80 + -18t + -1t2 = 18t + -18t + t2 + -1t2

Combine like terms: 18t + -18t = 0
-80 + -18t + -1t2 = 0 + t2 + -1t2
-80 + -18t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-80 + -18t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(80 + 18t + t2) = 0

Factor a trinomial.
-1((10 + t)(8 + t)) = 0

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

Simplifying
8 + t = 0

Solving
8 + t = 0

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

Add '-8' to each side of the equation.
8 + -8 + t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + t = 0 + -8
t = 0 + -8

Combine like terms: 0 + -8 = -8
t = -8

Simplifying
t = -8
Solution
t = {-10, -8}