0=-16t^2+48t+120

Solution for 0=-16t^2+48t+120 equation:

Simplifying
0 = -16t2 + 48t + 120

Reorder the terms:
0 = 120 + 48t + -16t2

Solving
0 = 120 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -120 = -120
-120 + -48t + 16t2 = 120 + 48t + -16t2 + -120 + -48t + 16t2

Reorder the terms:
-120 + -48t + 16t2 = 120 + -120 + 48t + -48t + -16t2 + 16t2

Combine like terms: 120 + -120 = 0
-120 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
-120 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-120 + -48t + 16t2 = 0 + -16t2 + 16t2
-120 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-120 + -48t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-15 + -6t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-15 + -6t + 2t2)' equal to zero and attempt to solve:

Simplifying
-15 + -6t + 2t2 = 0

Solving
-15 + -6t + 2t2 = 0

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

Divide each side by '2'.
-7.5 + -3t + t2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -3t + 7.5 + t2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -3t + t2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -3t + t2 = 0 + 7.5
-3t + t2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-3t + t2 = 7.5

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 7.5 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 7.5 + 2.25

Combine like terms: 7.5 + 2.25 = 9.75
2.25 + -3t + t2 = 9.75

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(t + -1.5) equal to 3.122498999 and -3.122498999.

Subproblem 1
t + -1.5 = 3.122498999

Simplifying
t + -1.5 = 3.122498999

Reorder the terms:
-1.5 + t = 3.122498999

Solving
-1.5 + t = 3.122498999

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = 3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 3.122498999 + 1.5
t = 3.122498999 + 1.5

Combine like terms: 3.122498999 + 1.5 = 4.622498999
t = 4.622498999

Simplifying
t = 4.622498999

Subproblem 2
t + -1.5 = -3.122498999

Simplifying
t + -1.5 = -3.122498999

Reorder the terms:
-1.5 + t = -3.122498999

Solving
-1.5 + t = -3.122498999

Solving for variable 't'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + t = -3.122498999 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -3.122498999 + 1.5
t = -3.122498999 + 1.5

Combine like terms: -3.122498999 + 1.5 = -1.622498999
t = -1.622498999

Simplifying
t = -1.622498999

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.622498999, -1.622498999}
Solution
t = {4.622498999, -1.622498999}