53=-16t^2+64t+5

Solution for 53=-16t^2+64t+5 equation:

Simplifying
53 = -16t2 + 64t + 5

Reorder the terms:
53 = 5 + 64t + -16t2

Solving
53 = 5 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 53 + -5 = 48
48 + -64t + 16t2 = 5 + 64t + -16t2 + -5 + -64t + 16t2

Reorder the terms:
48 + -64t + 16t2 = 5 + -5 + 64t + -64t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
48 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
48 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
48 + -64t + 16t2 = 0 + -16t2 + 16t2
48 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
48 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(3 + -4t + t2) = 0

Factor a trinomial.
16((1 + -1t)(3 + -1t)) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve:

Simplifying
1 + -1t = 0

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

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

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

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

Simplifying
t = 1
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 = {1, 3}