4t^2-5t-9=0

Solution for 4t^2-5t-9=0 equation:

Simplifying
4t2 + -5t + -9 = 0

Reorder the terms:
-9 + -5t + 4t2 = 0

Solving
-9 + -5t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -1t)(9 + -4t) = 0

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

Simplifying
-1 + -1t = 0

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

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

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

Divide each side by '-1'.
t = -1

Simplifying
t = -1
Subproblem 2
Set the factor '(9 + -4t)' equal to zero and attempt to solve:

Simplifying
9 + -4t = 0

Solving
9 + -4t = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4t = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4t = 0 + -9
-4t = 0 + -9

Combine like terms: 0 + -9 = -9
-4t = -9

Divide each side by '-4'.
t = 2.25

Simplifying
t = 2.25
Solution
t = {-1, 2.25}