6-2t^2=9t+15

Solution for 6-2t^2=9t+15 equation:

Simplifying
6 + -2t2 = 9t + 15

Reorder the terms:
6 + -2t2 = 15 + 9t

Solving
6 + -2t2 = 15 + 9t

Solving for variable 't'.

Reorder the terms:
6 + -15 + -9t + -2t2 = 15 + 9t + -15 + -9t

Combine like terms: 6 + -15 = -9
-9 + -9t + -2t2 = 15 + 9t + -15 + -9t

Reorder the terms:
-9 + -9t + -2t2 = 15 + -15 + 9t + -9t

Combine like terms: 15 + -15 = 0
-9 + -9t + -2t2 = 0 + 9t + -9t
-9 + -9t + -2t2 = 9t + -9t

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 9t + 2t2) = 0

Factor a trinomial.
-1((3 + t)(3 + 2t)) = 0

Ignore the factor -1.
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}