(7n-2)-(-3n+1)=-3n(1-3n)

Solution for (7n-2)-(-3n+1)=-3n(1-3n) equation:

Simplifying
(7n + -2) + -1(-3n + 1) = -3n(1 + -3n)

Reorder the terms:
(-2 + 7n) + -1(-3n + 1) = -3n(1 + -3n)

Remove parenthesis around (-2 + 7n)
-2 + 7n + -1(-3n + 1) = -3n(1 + -3n)

Reorder the terms:
-2 + 7n + -1(1 + -3n) = -3n(1 + -3n)
-2 + 7n + (1 * -1 + -3n * -1) = -3n(1 + -3n)
-2 + 7n + (-1 + 3n) = -3n(1 + -3n)

Reorder the terms:
-2 + -1 + 7n + 3n = -3n(1 + -3n)

Combine like terms: -2 + -1 = -3
-3 + 7n + 3n = -3n(1 + -3n)

Combine like terms: 7n + 3n = 10n
-3 + 10n = -3n(1 + -3n)
-3 + 10n = (1 * -3n + -3n * -3n)
-3 + 10n = (-3n + 9n2)

Solving
-3 + 10n = -3n + 9n2

Solving for variable 'n'.

Combine like terms: 10n + 3n = 13n
-3 + 13n + -9n2 = -3n + 9n2 + 3n + -9n2

Reorder the terms:
-3 + 13n + -9n2 = -3n + 3n + 9n2 + -9n2

Combine like terms: -3n + 3n = 0
-3 + 13n + -9n2 = 0 + 9n2 + -9n2
-3 + 13n + -9n2 = 9n2 + -9n2

Combine like terms: 9n2 + -9n2 = 0
-3 + 13n + -9n2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.3333333333 + -1.444444444n + n2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.444444444n + -0.3333333333 + n2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.444444444n + n2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.444444444n + n2 = 0 + -0.3333333333
-1.444444444n + n2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.444444444n + n2 = -0.3333333333

The n term is -1.444444444n.  Take half its coefficient (-0.722222222).
Square it (0.5216049380) and add it to both sides.

Add '0.5216049380' to each side of the equation.
-1.444444444n + 0.5216049380 + n2 = -0.3333333333 + 0.5216049380

Reorder the terms:
0.5216049380 + -1.444444444n + n2 = -0.3333333333 + 0.5216049380

Combine like terms: -0.3333333333 + 0.5216049380 = 0.1882716047
0.5216049380 + -1.444444444n + n2 = 0.1882716047

Factor a perfect square on the left side:
(n + -0.722222222)(n + -0.722222222) = 0.1882716047

Calculate the square root of the right side: 0.433902759

Break this problem into two subproblems by setting 
(n + -0.722222222) equal to 0.433902759 and -0.433902759.

Subproblem 1
n + -0.722222222 = 0.433902759

Simplifying
n + -0.722222222 = 0.433902759

Reorder the terms:
-0.722222222 + n = 0.433902759

Solving
-0.722222222 + n = 0.433902759

Solving for variable 'n'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + n = 0.433902759 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + n = 0.433902759 + 0.722222222
n = 0.433902759 + 0.722222222

Combine like terms: 0.433902759 + 0.722222222 = 1.156124981
n = 1.156124981

Simplifying
n = 1.156124981

Subproblem 2
n + -0.722222222 = -0.433902759

Simplifying
n + -0.722222222 = -0.433902759

Reorder the terms:
-0.722222222 + n = -0.433902759

Solving
-0.722222222 + n = -0.433902759

Solving for variable 'n'.

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

Add '0.722222222' to each side of the equation.
-0.722222222 + 0.722222222 + n = -0.433902759 + 0.722222222

Combine like terms: -0.722222222 + 0.722222222 = 0.000000000
0.000000000 + n = -0.433902759 + 0.722222222
n = -0.433902759 + 0.722222222

Combine like terms: -0.433902759 + 0.722222222 = 0.288319463
n = 0.288319463

Simplifying
n = 0.288319463

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.156124981, 0.288319463}