(-9-6+7n-4)3n-15=

Solution for (-9-6+7n-4)3n-15= equation:

Simplifying
(-9 + -6 + 7n + -4) * 3n + -15 = 0

Reorder the terms:
(-9 + -6 + -4 + 7n) * 3n + -15 = 0

Combine like terms: -9 + -6 = -15
(-15 + -4 + 7n) * 3n + -15 = 0

Combine like terms: -15 + -4 = -19
(-19 + 7n) * 3n + -15 = 0

Reorder the terms for easier multiplication:
3n(-19 + 7n) + -15 = 0
(-19 * 3n + 7n * 3n) + -15 = 0
(-57n + 21n2) + -15 = 0

Reorder the terms:
-15 + -57n + 21n2 = 0

Solving
-15 + -57n + 21n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -19n + 7n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -19n + 7n2)' equal to zero and attempt to solve:

Simplifying
-5 + -19n + 7n2 = 0

Solving
-5 + -19n + 7n2 = 0

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

Divide each side by '7'.
-0.7142857143 + -2.714285714n + n2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -2.714285714n + 0.7142857143 + n2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -2.714285714n + n2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -2.714285714n + n2 = 0 + 0.7142857143
-2.714285714n + n2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-2.714285714n + n2 = 0.7142857143

The n term is -2.714285714n.  Take half its coefficient (-1.357142857).
Square it (1.841836734) and add it to both sides.

Add '1.841836734' to each side of the equation.
-2.714285714n + 1.841836734 + n2 = 0.7142857143 + 1.841836734

Reorder the terms:
1.841836734 + -2.714285714n + n2 = 0.7142857143 + 1.841836734

Combine like terms: 0.7142857143 + 1.841836734 = 2.5561224483
1.841836734 + -2.714285714n + n2 = 2.5561224483

Factor a perfect square on the left side:
(n + -1.357142857)(n + -1.357142857) = 2.5561224483

Calculate the square root of the right side: 1.598787806

Break this problem into two subproblems by setting 
(n + -1.357142857) equal to 1.598787806 and -1.598787806.

Subproblem 1
n + -1.357142857 = 1.598787806

Simplifying
n + -1.357142857 = 1.598787806

Reorder the terms:
-1.357142857 + n = 1.598787806

Solving
-1.357142857 + n = 1.598787806

Solving for variable 'n'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + n = 1.598787806 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + n = 1.598787806 + 1.357142857
n = 1.598787806 + 1.357142857

Combine like terms: 1.598787806 + 1.357142857 = 2.955930663
n = 2.955930663

Simplifying
n = 2.955930663

Subproblem 2
n + -1.357142857 = -1.598787806

Simplifying
n + -1.357142857 = -1.598787806

Reorder the terms:
-1.357142857 + n = -1.598787806

Solving
-1.357142857 + n = -1.598787806

Solving for variable 'n'.

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

Add '1.357142857' to each side of the equation.
-1.357142857 + 1.357142857 + n = -1.598787806 + 1.357142857

Combine like terms: -1.357142857 + 1.357142857 = 0.000000000
0.000000000 + n = -1.598787806 + 1.357142857
n = -1.598787806 + 1.357142857

Combine like terms: -1.598787806 + 1.357142857 = -0.241644949
n = -0.241644949

Simplifying
n = -0.241644949

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.955930663, -0.241644949}
Solution
n = {2.955930663, -0.241644949}