t^2+19t+90=0

Solution for t^2+19t+90=0 equation:

Simplifying
t2 + 19t + 90 = 0

Reorder the terms:
90 + 19t + t2 = 0

Solving
90 + 19t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(10 + t)(9 + 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 '(9 + t)' equal to zero and attempt to solve:

Simplifying
9 + t = 0

Solving
9 + t = 0

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

Add '-9' to each side of the equation.
9 + -9 + t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + t = 0 + -9
t = 0 + -9

Combine like terms: 0 + -9 = -9
t = -9

Simplifying
t = -9
Solution
t = {-10, -9}