-73=5(n-4+7)(1+n)

Solution for -73=5(n-4+7)(1+n) equation:

Simplifying
-73 = 5(n + -4 + 7)(1 + n)

Reorder the terms:
-73 = 5(-4 + 7 + n)(1 + n)

Combine like terms: -4 + 7 = 3
-73 = 5(3 + n)(1 + n)

Multiply (3 + n) * (1 + n)
-73 = 5(3(1 + n) + n(1 + n))
-73 = 5((1 * 3 + n * 3) + n(1 + n))
-73 = 5((3 + 3n) + n(1 + n))
-73 = 5(3 + 3n + (1 * n + n * n))
-73 = 5(3 + 3n + (1n + n2))

Combine like terms: 3n + 1n = 4n
-73 = 5(3 + 4n + n2)
-73 = (3 * 5 + 4n * 5 + n2 * 5)
-73 = (15 + 20n + 5n2)

Solving
-73 = 15 + 20n + 5n2

Solving for variable 'n'.

Combine like terms: -73 + -15 = -88
-88 + -20n + -5n2 = 15 + 20n + 5n2 + -15 + -20n + -5n2

Reorder the terms:
-88 + -20n + -5n2 = 15 + -15 + 20n + -20n + 5n2 + -5n2

Combine like terms: 15 + -15 = 0
-88 + -20n + -5n2 = 0 + 20n + -20n + 5n2 + -5n2
-88 + -20n + -5n2 = 20n + -20n + 5n2 + -5n2

Combine like terms: 20n + -20n = 0
-88 + -20n + -5n2 = 0 + 5n2 + -5n2
-88 + -20n + -5n2 = 5n2 + -5n2

Combine like terms: 5n2 + -5n2 = 0
-88 + -20n + -5n2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(88 + 20n + 5n2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(88 + 20n + 5n2)' equal to zero and attempt to solve:

Simplifying
88 + 20n + 5n2 = 0

Solving
88 + 20n + 5n2 = 0

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

Divide each side by '5'.
17.6 + 4n + n2 = 0

Move the constant term to the right:

Add '-17.6' to each side of the equation.
17.6 + 4n + -17.6 + n2 = 0 + -17.6

Reorder the terms:
17.6 + -17.6 + 4n + n2 = 0 + -17.6

Combine like terms: 17.6 + -17.6 = 0.0
0.0 + 4n + n2 = 0 + -17.6
4n + n2 = 0 + -17.6

Combine like terms: 0 + -17.6 = -17.6
4n + n2 = -17.6

The n term is 4n.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4n + 4 + n2 = -17.6 + 4

Reorder the terms:
4 + 4n + n2 = -17.6 + 4

Combine like terms: -17.6 + 4 = -13.6
4 + 4n + n2 = -13.6

Factor a perfect square on the left side:
(n + 2)(n + 2) = -13.6

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.