5t^2-6t-8=0

Solution for 5t^2-6t-8=0 equation:

Simplifying
5t2 + -6t + -8 = 0

Reorder the terms:
-8 + -6t + 5t2 = 0

Solving
-8 + -6t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-4 + -5t)(2 + -1t) = 0

Subproblem 1
Set the factor '(-4 + -5t)' equal to zero and attempt to solve:

Simplifying
-4 + -5t = 0

Solving
-4 + -5t = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5t = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5t = 0 + 4
-5t = 0 + 4

Combine like terms: 0 + 4 = 4
-5t = 4

Divide each side by '-5'.
t = -0.8

Simplifying
t = -0.8
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 = {-0.8, 2}