t^2+19t+90t=0

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

Simplifying
t2 + 19t + 90t = 0

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

Combine like terms: 19t + 90t = 109t
109t + t2 = 0

Solving
109t + t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(109 + t) = 0

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0
Subproblem 2
Set the factor '(109 + t)' equal to zero and attempt to solve:

Simplifying
109 + t = 0

Solving
109 + t = 0

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

Add '-109' to each side of the equation.
109 + -109 + t = 0 + -109

Combine like terms: 109 + -109 = 0
0 + t = 0 + -109
t = 0 + -109

Combine like terms: 0 + -109 = -109
t = -109

Simplifying
t = -109
Solution
t = {0, -109}