2t^2+9t=-9

Solution for 2t^2+9t=-9 equation:

Simplifying
2t2 + 9t = -9

Reorder the terms:
9t + 2t2 = -9

Solving
9t + 2t2 = -9

Solving for variable 't'.

Reorder the terms:
9 + 9t + 2t2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 9t + 2t2 = 0

Factor a trinomial.
(3 + t)(3 + 2t) = 0

Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

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

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

Simplifying
t = -3
Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2t = 0 + -3

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

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

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Solution
t = {-3, -1.5}