(8n^2-3n+10)+(-3n-6n-7)=

Solution for (8n^2-3n+10)+(-3n-6n-7)= equation:

Simplifying
(8n2 + -3n + 10) + (-3n + -6n + -7) = 0

Reorder the terms:
(10 + -3n + 8n2) + (-3n + -6n + -7) = 0

Remove parenthesis around (10 + -3n + 8n2)
10 + -3n + 8n2 + (-3n + -6n + -7) = 0

Reorder the terms:
10 + -3n + 8n2 + (-7 + -3n + -6n) = 0

Combine like terms: -3n + -6n = -9n
10 + -3n + 8n2 + (-7 + -9n) = 0

Remove parenthesis around (-7 + -9n)
10 + -3n + 8n2 + -7 + -9n = 0

Reorder the terms:
10 + -7 + -3n + -9n + 8n2 = 0

Combine like terms: 10 + -7 = 3
3 + -3n + -9n + 8n2 = 0

Combine like terms: -3n + -9n = -12n
3 + -12n + 8n2 = 0

Solving
3 + -12n + 8n2 = 0

Solving for variable 'n'.

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

Divide each side by '8'.
0.375 + -1.5n + n2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + -1.5n + -0.375 + n2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + -1.5n + n2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + -1.5n + n2 = 0 + -0.375
-1.5n + n2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
-1.5n + n2 = -0.375

The n term is -1.5n.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5n + 0.5625 + n2 = -0.375 + 0.5625

Reorder the terms:
0.5625 + -1.5n + n2 = -0.375 + 0.5625

Combine like terms: -0.375 + 0.5625 = 0.1875
0.5625 + -1.5n + n2 = 0.1875

Factor a perfect square on the left side:
(n + -0.75)(n + -0.75) = 0.1875

Calculate the square root of the right side: 0.433012702

Break this problem into two subproblems by setting 
(n + -0.75) equal to 0.433012702 and -0.433012702.

Subproblem 1
n + -0.75 = 0.433012702

Simplifying
n + -0.75 = 0.433012702

Reorder the terms:
-0.75 + n = 0.433012702

Solving
-0.75 + n = 0.433012702

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = 0.433012702 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = 0.433012702 + 0.75
n = 0.433012702 + 0.75

Combine like terms: 0.433012702 + 0.75 = 1.183012702
n = 1.183012702

Simplifying
n = 1.183012702

Subproblem 2
n + -0.75 = -0.433012702

Simplifying
n + -0.75 = -0.433012702

Reorder the terms:
-0.75 + n = -0.433012702

Solving
-0.75 + n = -0.433012702

Solving for variable 'n'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + n = -0.433012702 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + n = -0.433012702 + 0.75
n = -0.433012702 + 0.75

Combine like terms: -0.433012702 + 0.75 = 0.316987298
n = 0.316987298

Simplifying
n = 0.316987298

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.183012702, 0.316987298}