12=-16t^2+48t+32

Solution for 12=-16t^2+48t+32 equation:

Simplifying
12 = -16t2 + 48t + 32

Reorder the terms:
12 = 32 + 48t + -16t2

Solving
12 = 32 + 48t + -16t2

Solving for variable 't'.

Combine like terms: 12 + -32 = -20
-20 + -48t + 16t2 = 32 + 48t + -16t2 + -32 + -48t + 16t2

Reorder the terms:
-20 + -48t + 16t2 = 32 + -32 + 48t + -48t + -16t2 + 16t2

Combine like terms: 32 + -32 = 0
-20 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2
-20 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2

Combine like terms: 48t + -48t = 0
-20 + -48t + 16t2 = 0 + -16t2 + 16t2
-20 + -48t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-20 + -48t + 16t2 = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + -12t + 4t2)' equal to zero and attempt to solve:

Simplifying
-5 + -12t + 4t2 = 0

Solving
-5 + -12t + 4t2 = 0

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

Divide each side by '4'.
-1.25 + -3t + t2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -3t + 1.25 + t2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -3t + t2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -3t + t2 = 0 + 1.25
-3t + t2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-3t + t2 = 1.25

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 = 1.25 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 1.25 + 2.25

Combine like terms: 1.25 + 2.25 = 3.5
2.25 + -3t + t2 = 3.5

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 3.5

Calculate the square root of the right side: 1.870828693

Break this problem into two subproblems by setting 
(t + -1.5) equal to 1.870828693 and -1.870828693.

Subproblem 1
t + -1.5 = 1.870828693

Simplifying
t + -1.5 = 1.870828693

Reorder the terms:
-1.5 + t = 1.870828693

Solving
-1.5 + t = 1.870828693

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 = 1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = 1.870828693 + 1.5
t = 1.870828693 + 1.5

Combine like terms: 1.870828693 + 1.5 = 3.370828693
t = 3.370828693

Simplifying
t = 3.370828693

Subproblem 2
t + -1.5 = -1.870828693

Simplifying
t + -1.5 = -1.870828693

Reorder the terms:
-1.5 + t = -1.870828693

Solving
-1.5 + t = -1.870828693

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 = -1.870828693 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + t = -1.870828693 + 1.5
t = -1.870828693 + 1.5

Combine like terms: -1.870828693 + 1.5 = -0.370828693
t = -0.370828693

Simplifying
t = -0.370828693

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.370828693, -0.370828693}
Solution
t = {3.370828693, -0.370828693}