2t^2=-15t-22

Solution for 2t^2=-15t-22 equation:

Simplifying
2t2 = -15t + -22

Reorder the terms:
2t2 = -22 + -15t

Solving
2t2 = -22 + -15t

Solving for variable 't'.

Reorder the terms:
22 + 15t + 2t2 = -22 + -15t + 22 + 15t

Reorder the terms:
22 + 15t + 2t2 = -22 + 22 + -15t + 15t

Combine like terms: -22 + 22 = 0
22 + 15t + 2t2 = 0 + -15t + 15t
22 + 15t + 2t2 = -15t + 15t

Combine like terms: -15t + 15t = 0
22 + 15t + 2t2 = 0

Factor a trinomial.
(11 + 2t)(2 + t) = 0

Subproblem 1
Set the factor '(11 + 2t)' equal to zero and attempt to solve:

Simplifying
11 + 2t = 0

Solving
11 + 2t = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2t = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2t = 0 + -11
2t = 0 + -11

Combine like terms: 0 + -11 = -11
2t = -11

Divide each side by '2'.
t = -5.5

Simplifying
t = -5.5
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 = {-5.5, -2}