-16t^2+21t+20=0

Solution for -16t^2+21t+20=0 equation:

Simplifying
-16t2 + 21t + 20 = 0

Reorder the terms:
20 + 21t + -16t2 = 0

Solving
20 + 21t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-1.25 + -1.3125t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -1.3125t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -1.3125t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -1.3125t + t2 = 0 + 1.25
-1.3125t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-1.3125t + t2 = 1.25

The t term is -1.3125t.  Take half its coefficient (-0.65625).
Square it (0.4306640625) and add it to both sides.

Add '0.4306640625' to each side of the equation.
-1.3125t + 0.4306640625 + t2 = 1.25 + 0.4306640625

Reorder the terms:
0.4306640625 + -1.3125t + t2 = 1.25 + 0.4306640625

Combine like terms: 1.25 + 0.4306640625 = 1.6806640625
0.4306640625 + -1.3125t + t2 = 1.6806640625

Factor a perfect square on the left side:
(t + -0.65625)(t + -0.65625) = 1.6806640625

Calculate the square root of the right side: 1.296404282

Break this problem into two subproblems by setting 
(t + -0.65625) equal to 1.296404282 and -1.296404282.

Subproblem 1
t + -0.65625 = 1.296404282

Simplifying
t + -0.65625 = 1.296404282

Reorder the terms:
-0.65625 + t = 1.296404282

Solving
-0.65625 + t = 1.296404282

Solving for variable 't'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + t = 1.296404282 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + t = 1.296404282 + 0.65625
t = 1.296404282 + 0.65625

Combine like terms: 1.296404282 + 0.65625 = 1.952654282
t = 1.952654282

Simplifying
t = 1.952654282

Subproblem 2
t + -0.65625 = -1.296404282

Simplifying
t + -0.65625 = -1.296404282

Reorder the terms:
-0.65625 + t = -1.296404282

Solving
-0.65625 + t = -1.296404282

Solving for variable 't'.

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

Add '0.65625' to each side of the equation.
-0.65625 + 0.65625 + t = -1.296404282 + 0.65625

Combine like terms: -0.65625 + 0.65625 = 0.00000
0.00000 + t = -1.296404282 + 0.65625
t = -1.296404282 + 0.65625

Combine like terms: -1.296404282 + 0.65625 = -0.640154282
t = -0.640154282

Simplifying
t = -0.640154282

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.952654282, -0.640154282}