3n-32=n^2-6n+3

Solution for 3n-32=n^2-6n+3 equation:

Simplifying
3n + -32 = n2 + -6n + 3

Reorder the terms:
-32 + 3n = n2 + -6n + 3

Reorder the terms:
-32 + 3n = 3 + -6n + n2

Solving
-32 + 3n = 3 + -6n + n2

Solving for variable 'n'.

Reorder the terms:
-32 + -3 + 3n + 6n + -1n2 = 3 + -6n + n2 + -3 + 6n + -1n2

Combine like terms: -32 + -3 = -35
-35 + 3n + 6n + -1n2 = 3 + -6n + n2 + -3 + 6n + -1n2

Combine like terms: 3n + 6n = 9n
-35 + 9n + -1n2 = 3 + -6n + n2 + -3 + 6n + -1n2

Reorder the terms:
-35 + 9n + -1n2 = 3 + -3 + -6n + 6n + n2 + -1n2

Combine like terms: 3 + -3 = 0
-35 + 9n + -1n2 = 0 + -6n + 6n + n2 + -1n2
-35 + 9n + -1n2 = -6n + 6n + n2 + -1n2

Combine like terms: -6n + 6n = 0
-35 + 9n + -1n2 = 0 + n2 + -1n2
-35 + 9n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-35 + 9n + -1n2 = 0

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

Divide each side by '-1'.
35 + -9n + n2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -9n + -35 + n2 = 0 + -35

Reorder the terms:
35 + -35 + -9n + n2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -9n + n2 = 0 + -35
-9n + n2 = 0 + -35

Combine like terms: 0 + -35 = -35
-9n + n2 = -35

The n term is -9n.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9n + 20.25 + n2 = -35 + 20.25

Reorder the terms:
20.25 + -9n + n2 = -35 + 20.25

Combine like terms: -35 + 20.25 = -14.75
20.25 + -9n + n2 = -14.75

Factor a perfect square on the left side:
(n + -4.5)(n + -4.5) = -14.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.