4n-40=7n(-2n+2)

Solution for 4n-40=7n(-2n+2) equation:

Simplifying
4n + -40 = 7n(-2n + 2)

Reorder the terms:
-40 + 4n = 7n(-2n + 2)

Reorder the terms:
-40 + 4n = 7n(2 + -2n)
-40 + 4n = (2 * 7n + -2n * 7n)
-40 + 4n = (14n + -14n2)

Solving
-40 + 4n = 14n + -14n2

Solving for variable 'n'.

Combine like terms: 4n + -14n = -10n
-40 + -10n + 14n2 = 14n + -14n2 + -14n + 14n2

Reorder the terms:
-40 + -10n + 14n2 = 14n + -14n + -14n2 + 14n2

Combine like terms: 14n + -14n = 0
-40 + -10n + 14n2 = 0 + -14n2 + 14n2
-40 + -10n + 14n2 = -14n2 + 14n2

Combine like terms: -14n2 + 14n2 = 0
-40 + -10n + 14n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + -5n + 7n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-20 + -5n + 7n2)' equal to zero and attempt to solve:

Simplifying
-20 + -5n + 7n2 = 0

Solving
-20 + -5n + 7n2 = 0

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

Divide each side by '7'.
-2.857142857 + -0.7142857143n + n2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + -0.7142857143n + 2.857142857 + n2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + -0.7142857143n + n2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + -0.7142857143n + n2 = 0 + 2.857142857
-0.7142857143n + n2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
-0.7142857143n + n2 = 2.857142857

The n term is -0.7142857143n.  Take half its coefficient (-0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
-0.7142857143n + 0.1275510204 + n2 = 2.857142857 + 0.1275510204

Reorder the terms:
0.1275510204 + -0.7142857143n + n2 = 2.857142857 + 0.1275510204

Combine like terms: 2.857142857 + 0.1275510204 = 2.9846938774
0.1275510204 + -0.7142857143n + n2 = 2.9846938774

Factor a perfect square on the left side:
(n + -0.3571428572)(n + -0.3571428572) = 2.9846938774

Calculate the square root of the right side: 1.72762666

Break this problem into two subproblems by setting 
(n + -0.3571428572) equal to 1.72762666 and -1.72762666.

Subproblem 1
n + -0.3571428572 = 1.72762666

Simplifying
n + -0.3571428572 = 1.72762666

Reorder the terms:
-0.3571428572 + n = 1.72762666

Solving
-0.3571428572 + n = 1.72762666

Solving for variable 'n'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + n = 1.72762666 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + n = 1.72762666 + 0.3571428572
n = 1.72762666 + 0.3571428572

Combine like terms: 1.72762666 + 0.3571428572 = 2.0847695172
n = 2.0847695172

Simplifying
n = 2.0847695172

Subproblem 2
n + -0.3571428572 = -1.72762666

Simplifying
n + -0.3571428572 = -1.72762666

Reorder the terms:
-0.3571428572 + n = -1.72762666

Solving
-0.3571428572 + n = -1.72762666

Solving for variable 'n'.

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

Add '0.3571428572' to each side of the equation.
-0.3571428572 + 0.3571428572 + n = -1.72762666 + 0.3571428572

Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000
0.0000000000 + n = -1.72762666 + 0.3571428572
n = -1.72762666 + 0.3571428572

Combine like terms: -1.72762666 + 0.3571428572 = -1.3704838028
n = -1.3704838028

Simplifying
n = -1.3704838028

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {2.0847695172, -1.3704838028}
Solution
n = {2.0847695172, -1.3704838028}