t^2=-12-8t

Solution for t^2=-12-8t equation:

Simplifying
t2 = -12 + -8t

Solving
t2 = -12 + -8t

Solving for variable 't'.

Reorder the terms:
12 + 8t + t2 = -12 + -8t + 12 + 8t

Reorder the terms:
12 + 8t + t2 = -12 + 12 + -8t + 8t

Combine like terms: -12 + 12 = 0
12 + 8t + t2 = 0 + -8t + 8t
12 + 8t + t2 = -8t + 8t

Combine like terms: -8t + 8t = 0
12 + 8t + t2 = 0

Factor a trinomial.
(6 + t)(2 + t) = 0

Subproblem 1
Set the factor '(6 + t)' equal to zero and attempt to solve:

Simplifying
6 + t = 0

Solving
6 + t = 0

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

Add '-6' to each side of the equation.
6 + -6 + t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + t = 0 + -6
t = 0 + -6

Combine like terms: 0 + -6 = -6
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

Add '-2' to each side of the equation.
2 + -2 + t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + t = 0 + -2
t = 0 + -2

Combine like terms: 0 + -2 = -2
t = -2

Simplifying
t = -2
Solution
t = {-6, -2}