67.2=(7-n)(12-n)

Solution for 67.2=(7-n)(12-n) equation:

Simplifying
67.2 = (7 + -1n)(12 + -1n)

Multiply (7 + -1n) * (12 + -1n)
67.2 = (7(12 + -1n) + -1n * (12 + -1n))
67.2 = ((12 * 7 + -1n * 7) + -1n * (12 + -1n))
67.2 = ((84 + -7n) + -1n * (12 + -1n))
67.2 = (84 + -7n + (12 * -1n + -1n * -1n))
67.2 = (84 + -7n + (-12n + 1n2))

Combine like terms: -7n + -12n = -19n
67.2 = (84 + -19n + 1n2)

Solving
67.2 = 84 + -19n + 1n2

Solving for variable 'n'.

Combine like terms: 67.2 + -84 = -16.8
-16.8 + 19n + -1n2 = 84 + -19n + 1n2 + -84 + 19n + -1n2

Reorder the terms:
-16.8 + 19n + -1n2 = 84 + -84 + -19n + 19n + 1n2 + -1n2

Combine like terms: 84 + -84 = 0
-16.8 + 19n + -1n2 = 0 + -19n + 19n + 1n2 + -1n2
-16.8 + 19n + -1n2 = -19n + 19n + 1n2 + -1n2

Combine like terms: -19n + 19n = 0
-16.8 + 19n + -1n2 = 0 + 1n2 + -1n2
-16.8 + 19n + -1n2 = 1n2 + -1n2

Combine like terms: 1n2 + -1n2 = 0
-16.8 + 19n + -1n2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
16.8 + -19n + n2 = 0

Move the constant term to the right:

Add '-16.8' to each side of the equation.
16.8 + -19n + -16.8 + n2 = 0 + -16.8

Reorder the terms:
16.8 + -16.8 + -19n + n2 = 0 + -16.8

Combine like terms: 16.8 + -16.8 = 0.0
0.0 + -19n + n2 = 0 + -16.8
-19n + n2 = 0 + -16.8

Combine like terms: 0 + -16.8 = -16.8
-19n + n2 = -16.8

The n term is -19n.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19n + 90.25 + n2 = -16.8 + 90.25

Reorder the terms:
90.25 + -19n + n2 = -16.8 + 90.25

Combine like terms: -16.8 + 90.25 = 73.45
90.25 + -19n + n2 = 73.45

Factor a perfect square on the left side:
(n + -9.5)(n + -9.5) = 73.45

Calculate the square root of the right side: 8.570297544

Break this problem into two subproblems by setting 
(n + -9.5) equal to 8.570297544 and -8.570297544.

Subproblem 1
n + -9.5 = 8.570297544

Simplifying
n + -9.5 = 8.570297544

Reorder the terms:
-9.5 + n = 8.570297544

Solving
-9.5 + n = 8.570297544

Solving for variable 'n'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + n = 8.570297544 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + n = 8.570297544 + 9.5
n = 8.570297544 + 9.5

Combine like terms: 8.570297544 + 9.5 = 18.070297544
n = 18.070297544

Simplifying
n = 18.070297544

Subproblem 2
n + -9.5 = -8.570297544

Simplifying
n + -9.5 = -8.570297544

Reorder the terms:
-9.5 + n = -8.570297544

Solving
-9.5 + n = -8.570297544

Solving for variable 'n'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + n = -8.570297544 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + n = -8.570297544 + 9.5
n = -8.570297544 + 9.5

Combine like terms: -8.570297544 + 9.5 = 0.929702456
n = 0.929702456

Simplifying
n = 0.929702456

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {18.070297544, 0.929702456}