16t^2-86t+108=0

Solution for 16t^2-86t+108=0 equation:

Simplifying
16t2 + -86t + 108 = 0

Reorder the terms:
108 + -86t + 16t2 = 0

Solving
108 + -86t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(54 + -43t + 8t2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
t = {2, 3.375}