7n^2+15n+7=

Solution for 7n^2+15n+7= equation:

Simplifying
7n2 + 15n + 7 = 0

Reorder the terms:
7 + 15n + 7n2 = 0

Solving
7 + 15n + 7n2 = 0

Solving for variable 'n'.

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

Divide each side by '7'.
1 + 2.142857143n + n2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.142857143n + -1 + n2 = 0 + -1

Reorder the terms:
1 + -1 + 2.142857143n + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.142857143n + n2 = 0 + -1
2.142857143n + n2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.142857143n + n2 = -1

The n term is 2.142857143n.  Take half its coefficient (1.071428572).
Square it (1.147959185) and add it to both sides.

Add '1.147959185' to each side of the equation.
2.142857143n + 1.147959185 + n2 = -1 + 1.147959185

Reorder the terms:
1.147959185 + 2.142857143n + n2 = -1 + 1.147959185

Combine like terms: -1 + 1.147959185 = 0.147959185
1.147959185 + 2.142857143n + n2 = 0.147959185

Factor a perfect square on the left side:
(n + 1.071428572)(n + 1.071428572) = 0.147959185

Calculate the square root of the right side: 0.384654631

Break this problem into two subproblems by setting 
(n + 1.071428572) equal to 0.384654631 and -0.384654631.

Subproblem 1
n + 1.071428572 = 0.384654631

Simplifying
n + 1.071428572 = 0.384654631

Reorder the terms:
1.071428572 + n = 0.384654631

Solving
1.071428572 + n = 0.384654631

Solving for variable 'n'.

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

Add '-1.071428572' to each side of the equation.
1.071428572 + -1.071428572 + n = 0.384654631 + -1.071428572

Combine like terms: 1.071428572 + -1.071428572 = 0.000000000
0.000000000 + n = 0.384654631 + -1.071428572
n = 0.384654631 + -1.071428572

Combine like terms: 0.384654631 + -1.071428572 = -0.686773941
n = -0.686773941

Simplifying
n = -0.686773941

Subproblem 2
n + 1.071428572 = -0.384654631

Simplifying
n + 1.071428572 = -0.384654631

Reorder the terms:
1.071428572 + n = -0.384654631

Solving
1.071428572 + n = -0.384654631

Solving for variable 'n'.

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

Add '-1.071428572' to each side of the equation.
1.071428572 + -1.071428572 + n = -0.384654631 + -1.071428572

Combine like terms: 1.071428572 + -1.071428572 = 0.000000000
0.000000000 + n = -0.384654631 + -1.071428572
n = -0.384654631 + -1.071428572

Combine like terms: -0.384654631 + -1.071428572 = -1.456083203
n = -1.456083203

Simplifying
n = -1.456083203

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.686773941, -1.456083203}