t^2=-11t-24

Solution for t^2=-11t-24 equation:

Simplifying
t2 = -11t + -24

Reorder the terms:
t2 = -24 + -11t

Solving
t2 = -24 + -11t

Solving for variable 't'.

Reorder the terms:
24 + 11t + t2 = -24 + -11t + 24 + 11t

Reorder the terms:
24 + 11t + t2 = -24 + 24 + -11t + 11t

Combine like terms: -24 + 24 = 0
24 + 11t + t2 = 0 + -11t + 11t
24 + 11t + t2 = -11t + 11t

Combine like terms: -11t + 11t = 0
24 + 11t + t2 = 0

Factor a trinomial.
(8 + t)(3 + t) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {-8, -3}