16t^2-32t=212

Solution for 16t^2-32t=212 equation:

Simplifying
16t2 + -32t = 212

Reorder the terms:
-32t + 16t2 = 212

Solving
-32t + 16t2 = 212

Solving for variable 't'.

Reorder the terms:
-212 + -32t + 16t2 = 212 + -212

Combine like terms: 212 + -212 = 0
-212 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-53 + -8t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-53 + -8t + 4t2)' equal to zero and attempt to solve:

Simplifying
-53 + -8t + 4t2 = 0

Solving
-53 + -8t + 4t2 = 0

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

Divide each side by '4'.
-13.25 + -2t + t2 = 0

Move the constant term to the right:

Add '13.25' to each side of the equation.
-13.25 + -2t + 13.25 + t2 = 0 + 13.25

Reorder the terms:
-13.25 + 13.25 + -2t + t2 = 0 + 13.25

Combine like terms: -13.25 + 13.25 = 0.00
0.00 + -2t + t2 = 0 + 13.25
-2t + t2 = 0 + 13.25

Combine like terms: 0 + 13.25 = 13.25
-2t + t2 = 13.25

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 = 13.25 + 1

Reorder the terms:
1 + -2t + t2 = 13.25 + 1

Combine like terms: 13.25 + 1 = 14.25
1 + -2t + t2 = 14.25

Factor a perfect square on the left side:
(t + -1)(t + -1) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(t + -1) equal to 3.774917218 and -3.774917218.

Subproblem 1
t + -1 = 3.774917218

Simplifying
t + -1 = 3.774917218

Reorder the terms:
-1 + t = 3.774917218

Solving
-1 + t = 3.774917218

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 = 3.774917218 + 1

Combine like terms: -1 + 1 = 0
0 + t = 3.774917218 + 1
t = 3.774917218 + 1

Combine like terms: 3.774917218 + 1 = 4.774917218
t = 4.774917218

Simplifying
t = 4.774917218

Subproblem 2
t + -1 = -3.774917218

Simplifying
t + -1 = -3.774917218

Reorder the terms:
-1 + t = -3.774917218

Solving
-1 + t = -3.774917218

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 = -3.774917218 + 1

Combine like terms: -1 + 1 = 0
0 + t = -3.774917218 + 1
t = -3.774917218 + 1

Combine like terms: -3.774917218 + 1 = -2.774917218
t = -2.774917218

Simplifying
t = -2.774917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.774917218, -2.774917218}
Solution
t = {4.774917218, -2.774917218}