17=-16t^2+52t+5

Solution for 17=-16t^2+52t+5 equation:

Simplifying
17 = -16t2 + 52t + 5

Reorder the terms:
17 = 5 + 52t + -16t2

Solving
17 = 5 + 52t + -16t2

Solving for variable 't'.

Combine like terms: 17 + -5 = 12
12 + -52t + 16t2 = 5 + 52t + -16t2 + -5 + -52t + 16t2

Reorder the terms:
12 + -52t + 16t2 = 5 + -5 + 52t + -52t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
12 + -52t + 16t2 = 0 + 52t + -52t + -16t2 + 16t2
12 + -52t + 16t2 = 52t + -52t + -16t2 + 16t2

Combine like terms: 52t + -52t = 0
12 + -52t + 16t2 = 0 + -16t2 + 16t2
12 + -52t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
12 + -52t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -13t + 4t2) = 0

Factor a trinomial.
4((1 + -4t)(3 + -1t)) = 0

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

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4t = 0 + -1
-4t = 0 + -1

Combine like terms: 0 + -1 = -1
-4t = -1

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
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 = {0.25, 3}