t^2=-35-12t

Solution for t^2=-35-12t equation:

Simplifying
t2 = -35 + -12t

Solving
t2 = -35 + -12t

Solving for variable 't'.

Reorder the terms:
35 + 12t + t2 = -35 + -12t + 35 + 12t

Reorder the terms:
35 + 12t + t2 = -35 + 35 + -12t + 12t

Combine like terms: -35 + 35 = 0
35 + 12t + t2 = 0 + -12t + 12t
35 + 12t + t2 = -12t + 12t

Combine like terms: -12t + 12t = 0
35 + 12t + t2 = 0

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

Subproblem 1
Set the factor '(7 + t)' equal to zero and attempt to solve:

Simplifying
7 + t = 0

Solving
7 + t = 0

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

Add '-7' to each side of the equation.
7 + -7 + t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + t = 0 + -7
t = 0 + -7

Combine like terms: 0 + -7 = -7
t = -7

Simplifying
t = -7
Subproblem 2
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
Solution
t = {-7, -5}