t^2=-1-2t

Solution for t^2=-1-2t equation:

Simplifying
t2 = -1 + -2t

Solving
t2 = -1 + -2t

Solving for variable 't'.

Reorder the terms:
1 + 2t + t2 = -1 + -2t + 1 + 2t

Reorder the terms:
1 + 2t + t2 = -1 + 1 + -2t + 2t

Combine like terms: -1 + 1 = 0
1 + 2t + t2 = 0 + -2t + 2t
1 + 2t + t2 = -2t + 2t

Combine like terms: -2t + 2t = 0
1 + 2t + t2 = 0

Factor a trinomial.
(1 + t)(1 + t) = 0

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

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

Simplifying
1 + t = 0

Solving
1 + t = 0

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

Add '-1' to each side of the equation.
1 + -1 + t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0 + -1
t = 0 + -1

Combine like terms: 0 + -1 = -1
t = -1

Simplifying
t = -1
Solution
t = {-1, -1}