t^2+2=-3t

Solution for t^2+2=-3t equation:

Simplifying
t2 + 2 = -3t

Reorder the terms:
2 + t2 = -3t

Solving
2 + t2 = -3t

Solving for variable 't'.

Reorder the terms:
2 + 3t + t2 = -3t + 3t

Combine like terms: -3t + 3t = 0
2 + 3t + t2 = 0

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

Subproblem 1
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
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 = {-2, -1}