-16t^2+48t+6=0

Solution for -16t^2+48t+6=0 equation:

Simplifying
-16t2 + 48t + 6 = 0

Reorder the terms:
6 + 48t + -16t2 = 0

Solving
6 + 48t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 24t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 24t + -8t2)' equal to zero and attempt to solve:

Simplifying
3 + 24t + -8t2 = 0

Solving
3 + 24t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.375 + -3t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -3t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -3t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -3t + t2 = 0 + 0.375
-3t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-3t + t2 = 0.375

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 = 0.375 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 0.375 + 2.25

Combine like terms: 0.375 + 2.25 = 2.625
2.25 + -3t + t2 = 2.625

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 2.625

Calculate the square root of the right side: 1.620185175

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.620185175 and -1.620185175.

Subproblem 1
t + -1.5 = 1.620185175

Simplifying
t + -1.5 = 1.620185175

Reorder the terms:
-1.5 + t = 1.620185175

Solving
-1.5 + t = 1.620185175

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 = 1.620185175 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.620185175 + 1.5
t = 1.620185175 + 1.5

Combine like terms: 1.620185175 + 1.5 = 3.120185175
t = 3.120185175

Simplifying
t = 3.120185175

Subproblem 2
t + -1.5 = -1.620185175

Simplifying
t + -1.5 = -1.620185175

Reorder the terms:
-1.5 + t = -1.620185175

Solving
-1.5 + t = -1.620185175

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 = -1.620185175 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.620185175 + 1.5
t = -1.620185175 + 1.5

Combine like terms: -1.620185175 + 1.5 = -0.120185175
t = -0.120185175

Simplifying
t = -0.120185175

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.120185175, -0.120185175}
Solution
t = {3.120185175, -0.120185175}