272=16t^2+32t

Solution for 272=16t^2+32t equation:

Simplifying
272 = 16t2 + 32t

Reorder the terms:
272 = 32t + 16t2

Solving
272 = 32t + 16t2

Solving for variable 't'.

Reorder the terms:
272 + -32t + -16t2 = 32t + -32t + 16t2 + -16t2

Combine like terms: 32t + -32t = 0
272 + -32t + -16t2 = 0 + 16t2 + -16t2
272 + -32t + -16t2 = 16t2 + -16t2

Combine like terms: 16t2 + -16t2 = 0
272 + -32t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(17 + -2t + -1t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(17 + -2t + -1t2)' equal to zero and attempt to solve:

Simplifying
17 + -2t + -1t2 = 0

Solving
17 + -2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + 2t + t2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 2t + 17 + t2 = 0 + 17

Reorder the terms:
-17 + 17 + 2t + t2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 2t + t2 = 0 + 17
2t + t2 = 0 + 17

Combine like terms: 0 + 17 = 17
2t + t2 = 17

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 = 17 + 1

Reorder the terms:
1 + 2t + t2 = 17 + 1

Combine like terms: 17 + 1 = 18
1 + 2t + t2 = 18

Factor a perfect square on the left side:
(t + 1)(t + 1) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(t + 1) equal to 4.242640687 and -4.242640687.

Subproblem 1
t + 1 = 4.242640687

Simplifying
t + 1 = 4.242640687

Reorder the terms:
1 + t = 4.242640687

Solving
1 + t = 4.242640687

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 = 4.242640687 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4.242640687 + -1
t = 4.242640687 + -1

Combine like terms: 4.242640687 + -1 = 3.242640687
t = 3.242640687

Simplifying
t = 3.242640687

Subproblem 2
t + 1 = -4.242640687

Simplifying
t + 1 = -4.242640687

Reorder the terms:
1 + t = -4.242640687

Solving
1 + t = -4.242640687

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 = -4.242640687 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4.242640687 + -1
t = -4.242640687 + -1

Combine like terms: -4.242640687 + -1 = -5.242640687
t = -5.242640687

Simplifying
t = -5.242640687

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.242640687, -5.242640687}
Solution
t = {3.242640687, -5.242640687}