5n(n-6)=-83

Solution for 5n(n-6)=-83 equation:

Simplifying
5n(n + -6) = -83

Reorder the terms:
5n(-6 + n) = -83
(-6 * 5n + n * 5n) = -83
(-30n + 5n2) = -83

Solving
-30n + 5n2 = -83

Solving for variable 'n'.

Reorder the terms:
83 + -30n + 5n2 = -83 + 83

Combine like terms: -83 + 83 = 0
83 + -30n + 5n2 = 0

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

Divide each side by '5'.
16.6 + -6n + n2 = 0

Move the constant term to the right:

Add '-16.6' to each side of the equation.
16.6 + -6n + -16.6 + n2 = 0 + -16.6

Reorder the terms:
16.6 + -16.6 + -6n + n2 = 0 + -16.6

Combine like terms: 16.6 + -16.6 = 0.0
0.0 + -6n + n2 = 0 + -16.6
-6n + n2 = 0 + -16.6

Combine like terms: 0 + -16.6 = -16.6
-6n + n2 = -16.6

The n term is -6n.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6n + 9 + n2 = -16.6 + 9

Reorder the terms:
9 + -6n + n2 = -16.6 + 9

Combine like terms: -16.6 + 9 = -7.6
9 + -6n + n2 = -7.6

Factor a perfect square on the left side:
(n + -3)(n + -3) = -7.6

Can't calculate square root of the right side.

The solution to this equation could not be determined.