(16t^2-22t-3)=0

Solution for (16t^2-22t-3)=0 equation:

Simplifying
(16t2 + -22t + -3) = 0

Reorder the terms:
(-3 + -22t + 16t2) = 0

Remove parenthesis around (-3 + -22t + 16t2)
-3 + -22t + 16t2 = 0

Solving
-3 + -22t + 16t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -8t)(3 + -2t) = 0

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

Simplifying
-1 + -8t = 0

Solving
-1 + -8t = 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 + -8t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8t = 0 + 1
-8t = 0 + 1

Combine like terms: 0 + 1 = 1
-8t = 1

Divide each side by '-8'.
t = -0.125

Simplifying
t = -0.125
Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {-0.125, 1.5}