(6n^2-5n+1)+(n^2+9n-8)=

Solution for (6n^2-5n+1)+(n^2+9n-8)= equation:

Simplifying
(6n2 + -5n + 1) + (n2 + 9n + -8) = 0

Reorder the terms:
(1 + -5n + 6n2) + (n2 + 9n + -8) = 0

Remove parenthesis around (1 + -5n + 6n2)
1 + -5n + 6n2 + (n2 + 9n + -8) = 0

Reorder the terms:
1 + -5n + 6n2 + (-8 + 9n + n2) = 0

Remove parenthesis around (-8 + 9n + n2)
1 + -5n + 6n2 + -8 + 9n + n2 = 0

Reorder the terms:
1 + -8 + -5n + 9n + 6n2 + n2 = 0

Combine like terms: 1 + -8 = -7
-7 + -5n + 9n + 6n2 + n2 = 0

Combine like terms: -5n + 9n = 4n
-7 + 4n + 6n2 + n2 = 0

Combine like terms: 6n2 + n2 = 7n2
-7 + 4n + 7n2 = 0

Solving
-7 + 4n + 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 + 0.5714285714n + n2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.5714285714n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.5714285714n + n2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.5714285714n + n2 = 0 + 1
0.5714285714n + n2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.5714285714n + n2 = 1

The n term is 0.5714285714n.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714n + 0.08163265305 + n2 = 1 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714n + n2 = 1 + 0.08163265305

Combine like terms: 1 + 0.08163265305 = 1.08163265305
0.08163265305 + 0.5714285714n + n2 = 1.08163265305

Factor a perfect square on the left side:
(n + 0.2857142857)(n + 0.2857142857) = 1.08163265305

Calculate the square root of the right side: 1.040015698

Break this problem into two subproblems by setting 
(n + 0.2857142857) equal to 1.040015698 and -1.040015698.

Subproblem 1
n + 0.2857142857 = 1.040015698

Simplifying
n + 0.2857142857 = 1.040015698

Reorder the terms:
0.2857142857 + n = 1.040015698

Solving
0.2857142857 + n = 1.040015698

Solving for variable 'n'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + n = 1.040015698 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + n = 1.040015698 + -0.2857142857
n = 1.040015698 + -0.2857142857

Combine like terms: 1.040015698 + -0.2857142857 = 0.7543014123
n = 0.7543014123

Simplifying
n = 0.7543014123

Subproblem 2
n + 0.2857142857 = -1.040015698

Simplifying
n + 0.2857142857 = -1.040015698

Reorder the terms:
0.2857142857 + n = -1.040015698

Solving
0.2857142857 + n = -1.040015698

Solving for variable 'n'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + n = -1.040015698 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + n = -1.040015698 + -0.2857142857
n = -1.040015698 + -0.2857142857

Combine like terms: -1.040015698 + -0.2857142857 = -1.3257299837
n = -1.3257299837

Simplifying
n = -1.3257299837

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.7543014123, -1.3257299837}