2(n^2+n-17)=0

Solution for 2(n^2+n-17)=0 equation:

Simplifying
2(n2 + n + -17) = 0

Reorder the terms:
2(-17 + n + n2) = 0
(-17 * 2 + n * 2 + n2 * 2) = 0
(-34 + 2n + 2n2) = 0

Solving
-34 + 2n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + n + n2)' equal to zero and attempt to solve:

Simplifying
-17 + n + n2 = 0

Solving
-17 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + n + 17 + n2 = 0 + 17

Reorder the terms:
-17 + 17 + n + n2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + n + n2 = 0 + 17
n + n2 = 0 + 17

Combine like terms: 0 + 17 = 17
n + n2 = 17

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = 17 + 0.25

Reorder the terms:
0.25 + n + n2 = 17 + 0.25

Combine like terms: 17 + 0.25 = 17.25
0.25 + n + n2 = 17.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(n + 0.5) equal to 4.153311931 and -4.153311931.

Subproblem 1
n + 0.5 = 4.153311931

Simplifying
n + 0.5 = 4.153311931

Reorder the terms:
0.5 + n = 4.153311931

Solving
0.5 + n = 4.153311931

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 4.153311931 + -0.5
n = 4.153311931 + -0.5

Combine like terms: 4.153311931 + -0.5 = 3.653311931
n = 3.653311931

Simplifying
n = 3.653311931

Subproblem 2
n + 0.5 = -4.153311931

Simplifying
n + 0.5 = -4.153311931

Reorder the terms:
0.5 + n = -4.153311931

Solving
0.5 + n = -4.153311931

Solving for variable 'n'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -4.153311931 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -4.153311931 + -0.5
n = -4.153311931 + -0.5

Combine like terms: -4.153311931 + -0.5 = -4.653311931
n = -4.653311931

Simplifying
n = -4.653311931

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {3.653311931, -4.653311931}
Solution
n = {3.653311931, -4.653311931}