.3(n-5)=.4-.2n(n-7)

Solution for .3(n-5)=.4-.2n(n-7) equation:

Simplifying
0.3(n + -5) = 0.4 + -0.2n(n + -7)

Reorder the terms:
0.3(-5 + n) = 0.4 + -0.2n(n + -7)
(-5 * 0.3 + n * 0.3) = 0.4 + -0.2n(n + -7)
(-1.5 + 0.3n) = 0.4 + -0.2n(n + -7)

Reorder the terms:
-1.5 + 0.3n = 0.4 + -0.2n(-7 + n)
-1.5 + 0.3n = 0.4 + (-7 * -0.2n + n * -0.2n)
-1.5 + 0.3n = 0.4 + (1.4n + -0.2n2)

Solving
-1.5 + 0.3n = 0.4 + 1.4n + -0.2n2

Solving for variable 'n'.

Reorder the terms:
-1.5 + -0.4 + 0.3n + -1.4n + 0.2n2 = 0.4 + 1.4n + -0.2n2 + -0.4 + -1.4n + 0.2n2

Combine like terms: -1.5 + -0.4 = -1.9
-1.9 + 0.3n + -1.4n + 0.2n2 = 0.4 + 1.4n + -0.2n2 + -0.4 + -1.4n + 0.2n2

Combine like terms: 0.3n + -1.4n = -1.1n
-1.9 + -1.1n + 0.2n2 = 0.4 + 1.4n + -0.2n2 + -0.4 + -1.4n + 0.2n2

Reorder the terms:
-1.9 + -1.1n + 0.2n2 = 0.4 + -0.4 + 1.4n + -1.4n + -0.2n2 + 0.2n2

Combine like terms: 0.4 + -0.4 = 0.0
-1.9 + -1.1n + 0.2n2 = 0.0 + 1.4n + -1.4n + -0.2n2 + 0.2n2
-1.9 + -1.1n + 0.2n2 = 1.4n + -1.4n + -0.2n2 + 0.2n2

Combine like terms: 1.4n + -1.4n = 0.0
-1.9 + -1.1n + 0.2n2 = 0.0 + -0.2n2 + 0.2n2
-1.9 + -1.1n + 0.2n2 = -0.2n2 + 0.2n2

Combine like terms: -0.2n2 + 0.2n2 = 0.0
-1.9 + -1.1n + 0.2n2 = 0.0

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

Divide each side by '0.2'.
-9.5 + -5.5n + n2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -5.5n + 9.5 + n2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -5.5n + n2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -5.5n + n2 = 0 + 9.5
-5.5n + n2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-5.5n + n2 = 9.5

The n term is -5.5n.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5n + 7.5625 + n2 = 9.5 + 7.5625

Reorder the terms:
7.5625 + -5.5n + n2 = 9.5 + 7.5625

Combine like terms: 9.5 + 7.5625 = 17.0625
7.5625 + -5.5n + n2 = 17.0625

Factor a perfect square on the left side:
(n + -2.75)(n + -2.75) = 17.0625

Calculate the square root of the right side: 4.13067791

Break this problem into two subproblems by setting 
(n + -2.75) equal to 4.13067791 and -4.13067791.

Subproblem 1
n + -2.75 = 4.13067791

Simplifying
n + -2.75 = 4.13067791

Reorder the terms:
-2.75 + n = 4.13067791

Solving
-2.75 + n = 4.13067791

Solving for variable 'n'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + n = 4.13067791 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + n = 4.13067791 + 2.75
n = 4.13067791 + 2.75

Combine like terms: 4.13067791 + 2.75 = 6.88067791
n = 6.88067791

Simplifying
n = 6.88067791

Subproblem 2
n + -2.75 = -4.13067791

Simplifying
n + -2.75 = -4.13067791

Reorder the terms:
-2.75 + n = -4.13067791

Solving
-2.75 + n = -4.13067791

Solving for variable 'n'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + n = -4.13067791 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + n = -4.13067791 + 2.75
n = -4.13067791 + 2.75

Combine like terms: -4.13067791 + 2.75 = -1.38067791
n = -1.38067791

Simplifying
n = -1.38067791

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.88067791, -1.38067791}