16t^2+32t-224=0

Solution for 16t^2+32t-224=0 equation:

Simplifying
16t2 + 32t + -224 = 0

Reorder the terms:
-224 + 32t + 16t2 = 0

Solving
-224 + 32t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-14 + 2t + t2) = 0

Ignore the factor 16.
Subproblem 1
Set the factor '(-14 + 2t + t2)' equal to zero and attempt to solve:

Simplifying
-14 + 2t + t2 = 0

Solving
-14 + 2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 2t + 14 + t2 = 0 + 14

Reorder the terms:
-14 + 14 + 2t + t2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 2t + t2 = 0 + 14
2t + t2 = 0 + 14

Combine like terms: 0 + 14 = 14
2t + t2 = 14

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 = 14 + 1

Reorder the terms:
1 + 2t + t2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + 2t + t2 = 15

Factor a perfect square on the left side:
(t + 1)(t + 1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(t + 1) equal to 3.872983346 and -3.872983346.

Subproblem 1
t + 1 = 3.872983346

Simplifying
t + 1 = 3.872983346

Reorder the terms:
1 + t = 3.872983346

Solving
1 + t = 3.872983346

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 = 3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + t = 3.872983346 + -1
t = 3.872983346 + -1

Combine like terms: 3.872983346 + -1 = 2.872983346
t = 2.872983346

Simplifying
t = 2.872983346

Subproblem 2
t + 1 = -3.872983346

Simplifying
t + 1 = -3.872983346

Reorder the terms:
1 + t = -3.872983346

Solving
1 + t = -3.872983346

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 = -3.872983346 + -1

Combine like terms: 1 + -1 = 0
0 + t = -3.872983346 + -1
t = -3.872983346 + -1

Combine like terms: -3.872983346 + -1 = -4.872983346
t = -4.872983346

Simplifying
t = -4.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.872983346, -4.872983346}
Solution
t = {2.872983346, -4.872983346}