n^2-6n+3=2(3n-16)

Solution for n^2-6n+3=2(3n-16) equation:

Simplifying
n2 + -6n + 3 = 2(3n + -16)

Reorder the terms:
3 + -6n + n2 = 2(3n + -16)

Reorder the terms:
3 + -6n + n2 = 2(-16 + 3n)
3 + -6n + n2 = (-16 * 2 + 3n * 2)
3 + -6n + n2 = (-32 + 6n)

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

Solving for variable 'n'.

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

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

Combine like terms: -6n + -6n = -12n
35 + -12n + n2 = -32 + 6n + 32 + -6n

Reorder the terms:
35 + -12n + n2 = -32 + 32 + 6n + -6n

Combine like terms: -32 + 32 = 0
35 + -12n + n2 = 0 + 6n + -6n
35 + -12n + n2 = 6n + -6n

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

Factor a trinomial.
(5 + -1n)(7 + -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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

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