3(n-9)=2n(n-7)

Solution for 3(n-9)=2n(n-7) equation:

Simplifying
3(n + -9) = 2n(n + -7)

Reorder the terms:
3(-9 + n) = 2n(n + -7)
(-9 * 3 + n * 3) = 2n(n + -7)
(-27 + 3n) = 2n(n + -7)

Reorder the terms:
-27 + 3n = 2n(-7 + n)
-27 + 3n = (-7 * 2n + n * 2n)
-27 + 3n = (-14n + 2n2)

Solving
-27 + 3n = -14n + 2n2

Solving for variable 'n'.

Combine like terms: 3n + 14n = 17n
-27 + 17n + -2n2 = -14n + 2n2 + 14n + -2n2

Reorder the terms:
-27 + 17n + -2n2 = -14n + 14n + 2n2 + -2n2

Combine like terms: -14n + 14n = 0
-27 + 17n + -2n2 = 0 + 2n2 + -2n2
-27 + 17n + -2n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-27 + 17n + -2n2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
13.5 + -8.5n + n2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -8.5n + -13.5 + n2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -8.5n + n2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -8.5n + n2 = 0 + -13.5
-8.5n + n2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-8.5n + n2 = -13.5

The n term is -8.5n.  Take half its coefficient (-4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
-8.5n + 18.0625 + n2 = -13.5 + 18.0625

Reorder the terms:
18.0625 + -8.5n + n2 = -13.5 + 18.0625

Combine like terms: -13.5 + 18.0625 = 4.5625
18.0625 + -8.5n + n2 = 4.5625

Factor a perfect square on the left side:
(n + -4.25)(n + -4.25) = 4.5625

Calculate the square root of the right side: 2.136000936

Break this problem into two subproblems by setting 
(n + -4.25) equal to 2.136000936 and -2.136000936.

Subproblem 1
n + -4.25 = 2.136000936

Simplifying
n + -4.25 = 2.136000936

Reorder the terms:
-4.25 + n = 2.136000936

Solving
-4.25 + n = 2.136000936

Solving for variable 'n'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + n = 2.136000936 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + n = 2.136000936 + 4.25
n = 2.136000936 + 4.25

Combine like terms: 2.136000936 + 4.25 = 6.386000936
n = 6.386000936

Simplifying
n = 6.386000936

Subproblem 2
n + -4.25 = -2.136000936

Simplifying
n + -4.25 = -2.136000936

Reorder the terms:
-4.25 + n = -2.136000936

Solving
-4.25 + n = -2.136000936

Solving for variable 'n'.

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

Add '4.25' to each side of the equation.
-4.25 + 4.25 + n = -2.136000936 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + n = -2.136000936 + 4.25
n = -2.136000936 + 4.25

Combine like terms: -2.136000936 + 4.25 = 2.113999064
n = 2.113999064

Simplifying
n = 2.113999064

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.386000936, 2.113999064}