9=2t^2-3t

Solution for 9=2t^2-3t equation:

Simplifying
9 = 2t2 + -3t

Reorder the terms:
9 = -3t + 2t2

Solving
9 = -3t + 2t2

Solving for variable 't'.

Reorder the terms:
9 + 3t + -2t2 = -3t + 3t + 2t2 + -2t2

Combine like terms: -3t + 3t = 0
9 + 3t + -2t2 = 0 + 2t2 + -2t2
9 + 3t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
9 + 3t + -2t2 = 0

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

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
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}