16t^2-64t-12=72

Solution for 16t^2-64t-12=72 equation:

Simplifying
16t2 + -64t + -12 = 72

Reorder the terms:
-12 + -64t + 16t2 = 72

Solving
-12 + -64t + 16t2 = 72

Solving for variable 't'.

Reorder the terms:
-12 + -72 + -64t + 16t2 = 72 + -72

Combine like terms: -12 + -72 = -84
-84 + -64t + 16t2 = 72 + -72

Combine like terms: 72 + -72 = 0
-84 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -16t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-21 + -16t + 4t2)' equal to zero and attempt to solve:

Simplifying
-21 + -16t + 4t2 = 0

Solving
-21 + -16t + 4t2 = 0

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

Divide each side by '4'.
-5.25 + -4t + t2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -4t + 5.25 + t2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -4t + t2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -4t + t2 = 0 + 5.25
-4t + t2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-4t + t2 = 5.25

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 5.25 + 4

Reorder the terms:
4 + -4t + t2 = 5.25 + 4

Combine like terms: 5.25 + 4 = 9.25
4 + -4t + t2 = 9.25

Factor a perfect square on the left side:
(t + -2)(t + -2) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(t + -2) equal to 3.041381265 and -3.041381265.

Subproblem 1
t + -2 = 3.041381265

Simplifying
t + -2 = 3.041381265

Reorder the terms:
-2 + t = 3.041381265

Solving
-2 + t = 3.041381265

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = 3.041381265 + 2

Combine like terms: -2 + 2 = 0
0 + t = 3.041381265 + 2
t = 3.041381265 + 2

Combine like terms: 3.041381265 + 2 = 5.041381265
t = 5.041381265

Simplifying
t = 5.041381265

Subproblem 2
t + -2 = -3.041381265

Simplifying
t + -2 = -3.041381265

Reorder the terms:
-2 + t = -3.041381265

Solving
-2 + t = -3.041381265

Solving for variable 't'.

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

Add '2' to each side of the equation.
-2 + 2 + t = -3.041381265 + 2

Combine like terms: -2 + 2 = 0
0 + t = -3.041381265 + 2
t = -3.041381265 + 2

Combine like terms: -3.041381265 + 2 = -1.041381265
t = -1.041381265

Simplifying
t = -1.041381265

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.041381265, -1.041381265}
Solution
t = {5.041381265, -1.041381265}