9t^2-54t-19=0

Solution for 9t^2-54t-19=0 equation:

Simplifying
9t2 + -54t + -19 = 0

Reorder the terms:
-19 + -54t + 9t2 = 0

Solving
-19 + -54t + 9t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -3t)(19 + -3t) = 0

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

Simplifying
-1 + -3t = 0

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

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

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

Divide each side by '-3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Subproblem 2
Set the factor '(19 + -3t)' equal to zero and attempt to solve:

Simplifying
19 + -3t = 0

Solving
19 + -3t = 0

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

Add '-19' to each side of the equation.
19 + -19 + -3t = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -3t = 0 + -19
-3t = 0 + -19

Combine like terms: 0 + -19 = -19
-3t = -19

Divide each side by '-3'.
t = 6.333333333

Simplifying
t = 6.333333333
Solution
t = {-0.3333333333, 6.333333333}