(n-6)(n-2)=-9n+32

Solution for (n-6)(n-2)=-9n+32 equation:

Simplifying
(n + -6)(n + -2) = -9n + 32

Reorder the terms:
(-6 + n)(n + -2) = -9n + 32

Reorder the terms:
(-6 + n)(-2 + n) = -9n + 32

Multiply (-6 + n) * (-2 + n)
(-6(-2 + n) + n(-2 + n)) = -9n + 32
((-2 * -6 + n * -6) + n(-2 + n)) = -9n + 32
((12 + -6n) + n(-2 + n)) = -9n + 32
(12 + -6n + (-2 * n + n * n)) = -9n + 32
(12 + -6n + (-2n + n2)) = -9n + 32

Combine like terms: -6n + -2n = -8n
(12 + -8n + n2) = -9n + 32

Reorder the terms:
12 + -8n + n2 = 32 + -9n

Solving
12 + -8n + n2 = 32 + -9n

Solving for variable 'n'.

Reorder the terms:
12 + -32 + -8n + 9n + n2 = 32 + -9n + -32 + 9n

Combine like terms: 12 + -32 = -20
-20 + -8n + 9n + n2 = 32 + -9n + -32 + 9n

Combine like terms: -8n + 9n = 1n
-20 + 1n + n2 = 32 + -9n + -32 + 9n

Reorder the terms:
-20 + 1n + n2 = 32 + -32 + -9n + 9n

Combine like terms: 32 + -32 = 0
-20 + 1n + n2 = 0 + -9n + 9n
-20 + 1n + n2 = -9n + 9n

Combine like terms: -9n + 9n = 0
-20 + 1n + n2 = 0

Factor a trinomial.
(-5 + -1n)(4 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Solution
n = {-5, 4}