84=-16t^2+100t

Solution for 84=-16t^2+100t equation:

Simplifying
84 = -16t2 + 100t

Reorder the terms:
84 = 100t + -16t2

Solving
84 = 100t + -16t2

Solving for variable 't'.

Reorder the terms:
84 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2

Combine like terms: 100t + -100t = 0
84 + -100t + 16t2 = 0 + -16t2 + 16t2
84 + -100t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
84 + -100t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + -25t + 4t2) = 0

Factor a trinomial.
4((1 + -1t)(21 + -4t)) = 0

Ignore the factor 4.
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 '(21 + -4t)' equal to zero and attempt to solve:

Simplifying
21 + -4t = 0

Solving
21 + -4t = 0

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

Add '-21' to each side of the equation.
21 + -21 + -4t = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -4t = 0 + -21
-4t = 0 + -21

Combine like terms: 0 + -21 = -21
-4t = -21

Divide each side by '-4'.
t = 5.25

Simplifying
t = 5.25
Solution
t = {1, 5.25}