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

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

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

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

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

Solving for variable 'n'.

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

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

Combine like terms: 6n + 6n = 12n
-35 + 12n + -1n2 = 3 + -6n + n2 + -3 + 6n + -1n2

Reorder the terms:
-35 + 12n + -1n2 = 3 + -3 + -6n + 6n + n2 + -1n2

Combine like terms: 3 + -3 = 0
-35 + 12n + -1n2 = 0 + -6n + 6n + n2 + -1n2
-35 + 12n + -1n2 = -6n + 6n + n2 + -1n2

Combine like terms: -6n + 6n = 0
-35 + 12n + -1n2 = 0 + n2 + -1n2
-35 + 12n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-35 + 12n + -1n2 = 0

Factor a trinomial.
(-7 + n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-7 + n)' equal to zero and attempt to solve:

Simplifying
-7 + n = 0

Solving
-7 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + n = 0 + 7
n = 0 + 7

Combine like terms: 0 + 7 = 7
n = 7

Simplifying
n = 7
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {7, 5}