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

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

Simplifying
0 = -16t2 + 48t + 48

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

Solving
0 = 48 + 48t + -16t2

Solving for variable 't'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '16'.
16(-3 + -3t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-3 + -3t + t2)' equal to zero and attempt to solve:

Simplifying
-3 + -3t + t2 = 0

Solving
-3 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 3 + 2.25

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

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3t + t2 = 5.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(t + -1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
t + -1.5 = 2.291287847

Simplifying
t + -1.5 = 2.291287847

Reorder the terms:
-1.5 + t = 2.291287847

Solving
-1.5 + t = 2.291287847

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 = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 2.291287847 + 1.5
t = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
t = 3.791287847

Simplifying
t = 3.791287847

Subproblem 2
t + -1.5 = -2.291287847

Simplifying
t + -1.5 = -2.291287847

Reorder the terms:
-1.5 + t = -2.291287847

Solving
-1.5 + t = -2.291287847

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 = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -2.291287847 + 1.5
t = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
t = -0.791287847

Simplifying
t = -0.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.791287847, -0.791287847}
Solution
t = {3.791287847, -0.791287847}