t^2+t=-5-5t

Solution for t^2+t=-5-5t equation:

Simplifying
t2 + t = -5 + -5t

Reorder the terms:
t + t2 = -5 + -5t

Solving
t + t2 = -5 + -5t

Solving for variable 't'.

Reorder the terms:
5 + t + 5t + t2 = -5 + -5t + 5 + 5t

Combine like terms: t + 5t = 6t
5 + 6t + t2 = -5 + -5t + 5 + 5t

Reorder the terms:
5 + 6t + t2 = -5 + 5 + -5t + 5t

Combine like terms: -5 + 5 = 0
5 + 6t + t2 = 0 + -5t + 5t
5 + 6t + t2 = -5t + 5t

Combine like terms: -5t + 5t = 0
5 + 6t + t2 = 0

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

Subproblem 1
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
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 = {-5, -1}