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

Solution for 0.3n(n-5)=0.4-0.2(n-7) equation:

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

Reorder the terms:
0.3n(-5 + n) = 0.4 + -0.2(n + -7)
(-5 * 0.3n + n * 0.3n) = 0.4 + -0.2(n + -7)
(-1.5n + 0.3n2) = 0.4 + -0.2(n + -7)

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

Combine like terms: 0.4 + 1.4 = 1.8
-1.5n + 0.3n2 = 1.8 + -0.2n

Solving
-1.5n + 0.3n2 = 1.8 + -0.2n

Solving for variable 'n'.

Reorder the terms:
-1.8 + -1.5n + 0.2n + 0.3n2 = 1.8 + -0.2n + -1.8 + 0.2n

Combine like terms: -1.5n + 0.2n = -1.3n
-1.8 + -1.3n + 0.3n2 = 1.8 + -0.2n + -1.8 + 0.2n

Reorder the terms:
-1.8 + -1.3n + 0.3n2 = 1.8 + -1.8 + -0.2n + 0.2n

Combine like terms: 1.8 + -1.8 = 0.0
-1.8 + -1.3n + 0.3n2 = 0.0 + -0.2n + 0.2n
-1.8 + -1.3n + 0.3n2 = -0.2n + 0.2n

Combine like terms: -0.2n + 0.2n = 0.0
-1.8 + -1.3n + 0.3n2 = 0.0

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

Divide each side by '0.3'.
-6 + -4.333333333n + n2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4.333333333n + 6 + n2 = 0 + 6

Reorder the terms:
-6 + 6 + -4.333333333n + n2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4.333333333n + n2 = 0 + 6
-4.333333333n + n2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4.333333333n + n2 = 6

The n term is -4.333333333n.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333n + 4.694444446 + n2 = 6 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333n + n2 = 6 + 4.694444446

Combine like terms: 6 + 4.694444446 = 10.694444446
4.694444446 + -4.333333333n + n2 = 10.694444446

Factor a perfect square on the left side:
(n + -2.166666667)(n + -2.166666667) = 10.694444446

Calculate the square root of the right side: 3.270236145

Break this problem into two subproblems by setting 
(n + -2.166666667) equal to 3.270236145 and -3.270236145.

Subproblem 1
n + -2.166666667 = 3.270236145

Simplifying
n + -2.166666667 = 3.270236145

Reorder the terms:
-2.166666667 + n = 3.270236145

Solving
-2.166666667 + n = 3.270236145

Solving for variable 'n'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + n = 3.270236145 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + n = 3.270236145 + 2.166666667
n = 3.270236145 + 2.166666667

Combine like terms: 3.270236145 + 2.166666667 = 5.436902812
n = 5.436902812

Simplifying
n = 5.436902812

Subproblem 2
n + -2.166666667 = -3.270236145

Simplifying
n + -2.166666667 = -3.270236145

Reorder the terms:
-2.166666667 + n = -3.270236145

Solving
-2.166666667 + n = -3.270236145

Solving for variable 'n'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + n = -3.270236145 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + n = -3.270236145 + 2.166666667
n = -3.270236145 + 2.166666667

Combine like terms: -3.270236145 + 2.166666667 = -1.103569478
n = -1.103569478

Simplifying
n = -1.103569478

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.436902812, -1.103569478}