16t^2+72t=32

Solution for 16t^2+72t=32 equation:

Simplifying
16t2 + 72t = 32

Reorder the terms:
72t + 16t2 = 32

Solving
72t + 16t2 = 32

Solving for variable 't'.

Reorder the terms:
-32 + 72t + 16t2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + 72t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-4 + 9t + 2t2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-4 + 9t + 2t2)' equal to zero and attempt to solve:

Simplifying
-4 + 9t + 2t2 = 0

Solving
-4 + 9t + 2t2 = 0

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

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

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.5t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.5t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.5t + t2 = 0 + 2
4.5t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.5t + t2 = 2

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 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = 2 + 5.0625

Combine like terms: 2 + 5.0625 = 7.0625
5.0625 + 4.5t + t2 = 7.0625

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(t + 2.25) equal to 2.657536453 and -2.657536453.

Subproblem 1
t + 2.25 = 2.657536453

Simplifying
t + 2.25 = 2.657536453

Reorder the terms:
2.25 + t = 2.657536453

Solving
2.25 + t = 2.657536453

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 = 2.657536453 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 2.657536453 + -2.25
t = 2.657536453 + -2.25

Combine like terms: 2.657536453 + -2.25 = 0.407536453
t = 0.407536453

Simplifying
t = 0.407536453

Subproblem 2
t + 2.25 = -2.657536453

Simplifying
t + 2.25 = -2.657536453

Reorder the terms:
2.25 + t = -2.657536453

Solving
2.25 + t = -2.657536453

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 = -2.657536453 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -2.657536453 + -2.25
t = -2.657536453 + -2.25

Combine like terms: -2.657536453 + -2.25 = -4.907536453
t = -4.907536453

Simplifying
t = -4.907536453

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.407536453, -4.907536453}
Solution
t = {0.407536453, -4.907536453}