16t^2+72t+40=0

Solution for 16t^2+72t+40=0 equation:

Simplifying
16t2 + 72t + 40 = 0

Reorder the terms:
40 + 72t + 16t2 = 0

Solving
40 + 72t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(5 + 9t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(5 + 9t + 2t2)' equal to zero and attempt to solve:

Simplifying
5 + 9t + 2t2 = 0

Solving
5 + 9t + 2t2 = 0

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

Divide each side by '2'.
2.5 + 4.5t + t2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4.5t + -2.5 + t2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4.5t + t2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4.5t + t2 = 0 + -2.5
4.5t + t2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
4.5t + t2 = -2.5

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 = -2.5 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = -2.5 + 5.0625

Combine like terms: -2.5 + 5.0625 = 2.5625
5.0625 + 4.5t + t2 = 2.5625

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(t + 2.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
t + 2.25 = 1.600781059

Simplifying
t + 2.25 = 1.600781059

Reorder the terms:
2.25 + t = 1.600781059

Solving
2.25 + t = 1.600781059

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 = 1.600781059 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 1.600781059 + -2.25
t = 1.600781059 + -2.25

Combine like terms: 1.600781059 + -2.25 = -0.649218941
t = -0.649218941

Simplifying
t = -0.649218941

Subproblem 2
t + 2.25 = -1.600781059

Simplifying
t + 2.25 = -1.600781059

Reorder the terms:
2.25 + t = -1.600781059

Solving
2.25 + t = -1.600781059

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 = -1.600781059 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -1.600781059 + -2.25
t = -1.600781059 + -2.25

Combine like terms: -1.600781059 + -2.25 = -3.850781059
t = -3.850781059

Simplifying
t = -3.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.649218941, -3.850781059}
Solution
t = {-0.649218941, -3.850781059}