8t^2+11t-54=0

Solution for 8t^2+11t-54=0 equation:

Simplifying
8t2 + 11t + -54 = 0

Reorder the terms:
-54 + 11t + 8t2 = 0

Solving
-54 + 11t + 8t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-27 + -8t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-27 + -8t)' equal to zero and attempt to solve:

Simplifying
-27 + -8t = 0

Solving
-27 + -8t = 0

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

Add '27' to each side of the equation.
-27 + 27 + -8t = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -8t = 0 + 27
-8t = 0 + 27

Combine like terms: 0 + 27 = 27
-8t = 27

Divide each side by '-8'.
t = -3.375

Simplifying
t = -3.375
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-3.375, 2}