t^2=-32-12t

Solution for t^2=-32-12t equation:

Simplifying
t2 = -32 + -12t

Solving
t2 = -32 + -12t

Solving for variable 't'.

Reorder the terms:
32 + 12t + t2 = -32 + -12t + 32 + 12t

Reorder the terms:
32 + 12t + t2 = -32 + 32 + -12t + 12t

Combine like terms: -32 + 32 = 0
32 + 12t + t2 = 0 + -12t + 12t
32 + 12t + t2 = -12t + 12t

Combine like terms: -12t + 12t = 0
32 + 12t + t2 = 0

Factor a trinomial.
(8 + t)(4 + 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 '(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 = {-8, -4}