t^2=-20-9t

Solution for t^2=-20-9t equation:

Simplifying
t2 = -20 + -9t

Solving
t2 = -20 + -9t

Solving for variable 't'.

Reorder the terms:
20 + 9t + t2 = -20 + -9t + 20 + 9t

Reorder the terms:
20 + 9t + t2 = -20 + 20 + -9t + 9t

Combine like terms: -20 + 20 = 0
20 + 9t + t2 = 0 + -9t + 9t
20 + 9t + t2 = -9t + 9t

Combine like terms: -9t + 9t = 0
20 + 9t + t2 = 0

Factor a trinomial.
(5 + t)(4 + t) = 0

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 '(4 + t)' equal to zero and attempt to solve:

Simplifying
4 + t = 0

Solving
4 + t = 0

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

Add '-4' to each side of the equation.
4 + -4 + t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t = 0 + -4
t = 0 + -4

Combine like terms: 0 + -4 = -4
t = -4

Simplifying
t = -4
Solution
t = {-5, -4}