5-n(n-4)=3(n+2)

Solution for 5-n(n-4)=3(n+2) equation:

Simplifying
5 + -1n(n + -4) = 3(n + 2)

Reorder the terms:
5 + -1n(-4 + n) = 3(n + 2)
5 + (-4 * -1n + n * -1n) = 3(n + 2)
5 + (4n + -1n2) = 3(n + 2)

Reorder the terms:
5 + 4n + -1n2 = 3(2 + n)
5 + 4n + -1n2 = (2 * 3 + n * 3)
5 + 4n + -1n2 = (6 + 3n)

Solving
5 + 4n + -1n2 = 6 + 3n

Solving for variable 'n'.

Reorder the terms:
5 + -6 + 4n + -3n + -1n2 = 6 + 3n + -6 + -3n

Combine like terms: 5 + -6 = -1
-1 + 4n + -3n + -1n2 = 6 + 3n + -6 + -3n

Combine like terms: 4n + -3n = 1n
-1 + 1n + -1n2 = 6 + 3n + -6 + -3n

Reorder the terms:
-1 + 1n + -1n2 = 6 + -6 + 3n + -3n

Combine like terms: 6 + -6 = 0
-1 + 1n + -1n2 = 0 + 3n + -3n
-1 + 1n + -1n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-1 + 1n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

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

Move the constant term to the right:

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

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

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

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

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 = -1 + 0.25

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

Combine like terms: -1 + 0.25 = -0.75
0.25 + -1n + n2 = -0.75

Factor a perfect square on the left side:
(n + -0.5)(n + -0.5) = -0.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.