-7n(n+3)-8(1+8n)=

Solution for -7n(n+3)-8(1+8n)= equation:

Simplifying
-7n(n + 3) + -8(1 + 8n) = 0

Reorder the terms:
-7n(3 + n) + -8(1 + 8n) = 0
(3 * -7n + n * -7n) + -8(1 + 8n) = 0
(-21n + -7n2) + -8(1 + 8n) = 0
-21n + -7n2 + (1 * -8 + 8n * -8) = 0
-21n + -7n2 + (-8 + -64n) = 0

Reorder the terms:
-8 + -21n + -64n + -7n2 = 0

Combine like terms: -21n + -64n = -85n
-8 + -85n + -7n2 = 0

Solving
-8 + -85n + -7n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8 + 85n + 7n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(8 + 85n + 7n2)' equal to zero and attempt to solve:

Simplifying
8 + 85n + 7n2 = 0

Solving
8 + 85n + 7n2 = 0

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

Divide each side by '7'.
1.142857143 + 12.14285714n + n2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + 12.14285714n + -1.142857143 + n2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + 12.14285714n + n2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + 12.14285714n + n2 = 0 + -1.142857143
12.14285714n + n2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
12.14285714n + n2 = -1.142857143

The n term is 12.14285714n.  Take half its coefficient (6.07142857).
Square it (36.86224488) and add it to both sides.

Add '36.86224488' to each side of the equation.
12.14285714n + 36.86224488 + n2 = -1.142857143 + 36.86224488

Reorder the terms:
36.86224488 + 12.14285714n + n2 = -1.142857143 + 36.86224488

Combine like terms: -1.142857143 + 36.86224488 = 35.719387737
36.86224488 + 12.14285714n + n2 = 35.719387737

Factor a perfect square on the left side:
(n + 6.07142857)(n + 6.07142857) = 35.719387737

Calculate the square root of the right side: 5.976569897

Break this problem into two subproblems by setting 
(n + 6.07142857) equal to 5.976569897 and -5.976569897.

Subproblem 1
n + 6.07142857 = 5.976569897

Simplifying
n + 6.07142857 = 5.976569897

Reorder the terms:
6.07142857 + n = 5.976569897

Solving
6.07142857 + n = 5.976569897

Solving for variable 'n'.

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

Add '-6.07142857' to each side of the equation.
6.07142857 + -6.07142857 + n = 5.976569897 + -6.07142857

Combine like terms: 6.07142857 + -6.07142857 = 0.00000000
0.00000000 + n = 5.976569897 + -6.07142857
n = 5.976569897 + -6.07142857

Combine like terms: 5.976569897 + -6.07142857 = -0.094858673
n = -0.094858673

Simplifying
n = -0.094858673

Subproblem 2
n + 6.07142857 = -5.976569897

Simplifying
n + 6.07142857 = -5.976569897

Reorder the terms:
6.07142857 + n = -5.976569897

Solving
6.07142857 + n = -5.976569897

Solving for variable 'n'.

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

Add '-6.07142857' to each side of the equation.
6.07142857 + -6.07142857 + n = -5.976569897 + -6.07142857

Combine like terms: 6.07142857 + -6.07142857 = 0.00000000
0.00000000 + n = -5.976569897 + -6.07142857
n = -5.976569897 + -6.07142857

Combine like terms: -5.976569897 + -6.07142857 = -12.047998467
n = -12.047998467

Simplifying
n = -12.047998467

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.094858673, -12.047998467}
Solution
n = {-0.094858673, -12.047998467}