-16t^2+192t+100=0

Solution for -16t^2+192t+100=0 equation:

Simplifying
-16t2 + 192t + 100 = 0

Reorder the terms:
100 + 192t + -16t2 = 0

Solving
100 + 192t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 48t + -4t2) = 0

Factor a trinomial.
4((25 + -2t)(1 + 2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(25 + -2t)' equal to zero and attempt to solve:

Simplifying
25 + -2t = 0

Solving
25 + -2t = 0

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

Add '-25' to each side of the equation.
25 + -25 + -2t = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -2t = 0 + -25
-2t = 0 + -25

Combine like terms: 0 + -25 = -25
-2t = -25

Divide each side by '-2'.
t = 12.5

Simplifying
t = 12.5
Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 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 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {12.5, -0.5}