16t^2+10t-174=0

Solution for 16t^2+10t-174=0 equation:

Simplifying
16t2 + 10t + -174 = 0

Reorder the terms:
-174 + 10t + 16t2 = 0

Solving
-174 + 10t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-87 + 5t + 8t2) = 0

Factor a trinomial.
2((-29 + -8t)(3 + -1t)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-29 + -8t)' equal to zero and attempt to solve:

Simplifying
-29 + -8t = 0

Solving
-29 + -8t = 0

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

Add '29' to each side of the equation.
-29 + 29 + -8t = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -8t = 0 + 29
-8t = 0 + 29

Combine like terms: 0 + 29 = 29
-8t = 29

Divide each side by '-8'.
t = -3.625

Simplifying
t = -3.625
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

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

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-3.625, 3}