7(5-5n)5n=85

Solution for 7(5-5n)5n=85 equation:

Simplifying
7(5 + -5n) * 5n = 85

Reorder the terms for easier multiplication:
7 * 5n(5 + -5n) = 85

Multiply 7 * 5
35n(5 + -5n) = 85
(5 * 35n + -5n * 35n) = 85
(175n + -175n2) = 85

Solving
175n + -175n2 = 85

Solving for variable 'n'.

Reorder the terms:
-85 + 175n + -175n2 = 85 + -85

Combine like terms: 85 + -85 = 0
-85 + 175n + -175n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-17 + 35n + -35n2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-17 + 35n + -35n2)' equal to zero and attempt to solve:

Simplifying
-17 + 35n + -35n2 = 0

Solving
-17 + 35n + -35n2 = 0

Begin completing the square.  Divide all terms by
-35 the coefficient of the squared term: 

Divide each side by '-35'.
0.4857142857 + -1n + n2 = 0

Move the constant term to the right:

Add '-0.4857142857' to each side of the equation.
0.4857142857 + -1n + -0.4857142857 + n2 = 0 + -0.4857142857

Reorder the terms:
0.4857142857 + -0.4857142857 + -1n + n2 = 0 + -0.4857142857

Combine like terms: 0.4857142857 + -0.4857142857 = 0.0000000000
0.0000000000 + -1n + n2 = 0 + -0.4857142857
-1n + n2 = 0 + -0.4857142857

Combine like terms: 0 + -0.4857142857 = -0.4857142857
-1n + n2 = -0.4857142857

The n term is -1n.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1n + 0.25 + n2 = -0.4857142857 + 0.25

Reorder the terms:
0.25 + -1n + n2 = -0.4857142857 + 0.25

Combine like terms: -0.4857142857 + 0.25 = -0.2357142857
0.25 + -1n + n2 = -0.2357142857

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = -0.2357142857

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.