16t^2+72t+4=0

Solution for 16t^2+72t+4=0 equation:

Simplifying
16t2 + 72t + 4 = 0

Reorder the terms:
4 + 72t + 16t2 = 0

Solving
4 + 72t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 18t + 4t2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + 18t + 4t2)' equal to zero and attempt to solve:

Simplifying
1 + 18t + 4t2 = 0

Solving
1 + 18t + 4t2 = 0

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

Divide each side by '4'.
0.25 + 4.5t + t2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 4.5t + -0.25 + t2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 4.5t + t2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 4.5t + t2 = 0 + -0.25
4.5t + t2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
4.5t + t2 = -0.25

The t term is 4.5t.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5t + 5.0625 + t2 = -0.25 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = -0.25 + 5.0625

Combine like terms: -0.25 + 5.0625 = 4.8125
5.0625 + 4.5t + t2 = 4.8125

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 4.8125

Calculate the square root of the right side: 2.193741097

Break this problem into two subproblems by setting 
(t + 2.25) equal to 2.193741097 and -2.193741097.

Subproblem 1
t + 2.25 = 2.193741097

Simplifying
t + 2.25 = 2.193741097

Reorder the terms:
2.25 + t = 2.193741097

Solving
2.25 + t = 2.193741097

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = 2.193741097 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 2.193741097 + -2.25
t = 2.193741097 + -2.25

Combine like terms: 2.193741097 + -2.25 = -0.056258903
t = -0.056258903

Simplifying
t = -0.056258903

Subproblem 2
t + 2.25 = -2.193741097

Simplifying
t + 2.25 = -2.193741097

Reorder the terms:
2.25 + t = -2.193741097

Solving
2.25 + t = -2.193741097

Solving for variable 't'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + t = -2.193741097 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -2.193741097 + -2.25
t = -2.193741097 + -2.25

Combine like terms: -2.193741097 + -2.25 = -4.443741097
t = -4.443741097

Simplifying
t = -4.443741097

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.056258903, -4.443741097}
Solution
t = {-0.056258903, -4.443741097}