174=10t+16t^2

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

Simplifying
174 = 10t + 16t2

Solving
174 = 10t + 16t2

Solving for variable 't'.

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

Combine like terms: 10t + -10t = 0
174 + -10t + -16t2 = 0 + 16t2 + -16t2
174 + -10t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
174 + -10t + -16t2 = 0

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
t = {3, -3.625}