421=-16t^2+96t+277

Solution for 421=-16t^2+96t+277 equation:

Simplifying
421 = -16t2 + 96t + 277

Reorder the terms:
421 = 277 + 96t + -16t2

Solving
421 = 277 + 96t + -16t2

Solving for variable 't'.

Combine like terms: 421 + -277 = 144
144 + -96t + 16t2 = 277 + 96t + -16t2 + -277 + -96t + 16t2

Reorder the terms:
144 + -96t + 16t2 = 277 + -277 + 96t + -96t + -16t2 + 16t2

Combine like terms: 277 + -277 = 0
144 + -96t + 16t2 = 0 + 96t + -96t + -16t2 + 16t2
144 + -96t + 16t2 = 96t + -96t + -16t2 + 16t2

Combine like terms: 96t + -96t = 0
144 + -96t + 16t2 = 0 + -16t2 + 16t2
144 + -96t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
144 + -96t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(9 + -6t + t2) = 0

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

Ignore the factor 16.
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 '(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 = {3, 3}