0=20+76t-16t^2

Solution for 0=20+76t-16t^2 equation:

Simplifying
0 = 20 + 76t + -16t2

Solving
0 = 20 + 76t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -20 = -20
-20 + -76t + 16t2 = 20 + 76t + -16t2 + -20 + -76t + 16t2

Reorder the terms:
-20 + -76t + 16t2 = 20 + -20 + 76t + -76t + -16t2 + 16t2

Combine like terms: 20 + -20 = 0
-20 + -76t + 16t2 = 0 + 76t + -76t + -16t2 + 16t2
-20 + -76t + 16t2 = 76t + -76t + -16t2 + 16t2

Combine like terms: 76t + -76t = 0
-20 + -76t + 16t2 = 0 + -16t2 + 16t2
-20 + -76t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-20 + -76t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -19t + 4t2) = 0

Factor a trinomial.
4((-1 + -4t)(5 + -1t)) = 0

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

Simplifying
-1 + -4t = 0

Solving
-1 + -4t = 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 + -4t = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4t = 0 + 1
-4t = 0 + 1

Combine like terms: 0 + 1 = 1
-4t = 1

Divide each side by '-4'.
t = -0.25

Simplifying
t = -0.25
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-0.25, 5}