90+t^2+23t=0

Solution for 90+t^2+23t=0 equation:

Simplifying
90 + t2 + 23t = 0

Reorder the terms:
90 + 23t + t2 = 0

Solving
90 + 23t + t2 = 0

Solving for variable 't'.

Factor a trinomial.
(18 + t)(5 + t) = 0

Subproblem 1
Set the factor '(18 + t)' equal to zero and attempt to solve:

Simplifying
18 + t = 0

Solving
18 + t = 0

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

Add '-18' to each side of the equation.
18 + -18 + t = 0 + -18

Combine like terms: 18 + -18 = 0
0 + t = 0 + -18
t = 0 + -18

Combine like terms: 0 + -18 = -18
t = -18

Simplifying
t = -18
Subproblem 2
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
Solution
t = {-18, -5}