3n+1(n-6)=3n(n-5)

Solution for 3n+1(n-6)=3n(n-5) equation:

Simplifying
3n + 1(n + -6) = 3n(n + -5)

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

Reorder the terms:
-6 + 3n + 1n = 3n(n + -5)

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

Reorder the terms:
-6 + 4n = 3n(-5 + n)
-6 + 4n = (-5 * 3n + n * 3n)
-6 + 4n = (-15n + 3n2)

Solving
-6 + 4n = -15n + 3n2

Solving for variable 'n'.

Combine like terms: 4n + 15n = 19n
-6 + 19n + -3n2 = -15n + 3n2 + 15n + -3n2

Reorder the terms:
-6 + 19n + -3n2 = -15n + 15n + 3n2 + -3n2

Combine like terms: -15n + 15n = 0
-6 + 19n + -3n2 = 0 + 3n2 + -3n2
-6 + 19n + -3n2 = 3n2 + -3n2

Combine like terms: 3n2 + -3n2 = 0
-6 + 19n + -3n2 = 0

Factor a trinomial.
(-6 + n)(1 + -3n) = 0

Subproblem 1
Set the factor '(-6 + n)' equal to zero and attempt to solve:

Simplifying
-6 + n = 0

Solving
-6 + n = 0

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

Add '6' to each side of the equation.
-6 + 6 + n = 0 + 6

Combine like terms: -6 + 6 = 0
0 + n = 0 + 6
n = 0 + 6

Combine like terms: 0 + 6 = 6
n = 6

Simplifying
n = 6
Subproblem 2
Set the factor '(1 + -3n)' equal to zero and attempt to solve:

Simplifying
1 + -3n = 0

Solving
1 + -3n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
Solution
n = {6, 0.3333333333}