48t-16t^2-20=0

Solution for 48t-16t^2-20=0 equation:

Simplifying
48t + -16t2 + -20 = 0

Reorder the terms:
-20 + 48t + -16t2 = 0

Solving
-20 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 12t + -4t2) = 0

Factor a trinomial.
4((-5 + 2t)(1 + -2t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 2t)' equal to zero and attempt to solve:

Simplifying
-5 + 2t = 0

Solving
-5 + 2t = 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 + 2t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2t = 0 + 5
2t = 0 + 5

Combine like terms: 0 + 5 = 5
2t = 5

Divide each side by '2'.
t = 2.5

Simplifying
t = 2.5
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 = {2.5, 0.5}