-48=-16t^2+32t+48

Solution for -48=-16t^2+32t+48 equation:

Simplifying
-48 = -16t2 + 32t + 48

Reorder the terms:
-48 = 48 + 32t + -16t2

Solving
-48 = 48 + 32t + -16t2

Solving for variable 't'.

Combine like terms: -48 + -48 = -96
-96 + -32t + 16t2 = 48 + 32t + -16t2 + -48 + -32t + 16t2

Reorder the terms:
-96 + -32t + 16t2 = 48 + -48 + 32t + -32t + -16t2 + 16t2

Combine like terms: 48 + -48 = 0
-96 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-96 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-96 + -32t + 16t2 = 0 + -16t2 + 16t2
-96 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-96 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-6 + -2t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-6 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
-6 + -2t + t2 = 0

Solving
-6 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -2t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2t + t2 = 0 + 6
-2t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2t + t2 = 6

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 6 + 1

Reorder the terms:
1 + -2t + t2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2t + t2 = 7

Factor a perfect square on the left side:
(t + -1)(t + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + -1 = 2.645751311

Simplifying
t + -1 = 2.645751311

Reorder the terms:
-1 + t = 2.645751311

Solving
-1 + t = 2.645751311

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.645751311 + 1
t = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
t = 3.645751311

Simplifying
t = 3.645751311

Subproblem 2
t + -1 = -2.645751311

Simplifying
t + -1 = -2.645751311

Reorder the terms:
-1 + t = -2.645751311

Solving
-1 + t = -2.645751311

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.645751311 + 1
t = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
t = -1.645751311

Simplifying
t = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.645751311, -1.645751311}
Solution
t = {3.645751311, -1.645751311}