5n+4=7(n+1)*-2n

Solution for 5n+4=7(n+1)*-2n equation:

Simplifying
5n + 4 = 7(n + 1) * -2n

Reorder the terms:
4 + 5n = 7(n + 1) * -2n

Reorder the terms:
4 + 5n = 7(1 + n) * -2n

Reorder the terms for easier multiplication:
4 + 5n = 7 * -2n(1 + n)

Multiply 7 * -2
4 + 5n = -14n(1 + n)
4 + 5n = (1 * -14n + n * -14n)
4 + 5n = (-14n + -14n2)

Solving
4 + 5n = -14n + -14n2

Solving for variable 'n'.

Combine like terms: 5n + 14n = 19n
4 + 19n + 14n2 = -14n + -14n2 + 14n + 14n2

Reorder the terms:
4 + 19n + 14n2 = -14n + 14n + -14n2 + 14n2

Combine like terms: -14n + 14n = 0
4 + 19n + 14n2 = 0 + -14n2 + 14n2
4 + 19n + 14n2 = -14n2 + 14n2

Combine like terms: -14n2 + 14n2 = 0
4 + 19n + 14n2 = 0

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

Divide each side by '14'.
0.2857142857 + 1.357142857n + n2 = 0

Move the constant term to the right:

Add '-0.2857142857' to each side of the equation.
0.2857142857 + 1.357142857n + -0.2857142857 + n2 = 0 + -0.2857142857

Reorder the terms:
0.2857142857 + -0.2857142857 + 1.357142857n + n2 = 0 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + 1.357142857n + n2 = 0 + -0.2857142857
1.357142857n + n2 = 0 + -0.2857142857

Combine like terms: 0 + -0.2857142857 = -0.2857142857
1.357142857n + n2 = -0.2857142857

The n term is 1.357142857n.  Take half its coefficient (0.6785714285).
Square it (0.4604591836) and add it to both sides.

Add '0.4604591836' to each side of the equation.
1.357142857n + 0.4604591836 + n2 = -0.2857142857 + 0.4604591836

Reorder the terms:
0.4604591836 + 1.357142857n + n2 = -0.2857142857 + 0.4604591836

Combine like terms: -0.2857142857 + 0.4604591836 = 0.1747448979
0.4604591836 + 1.357142857n + n2 = 0.1747448979

Factor a perfect square on the left side:
(n + 0.6785714285)(n + 0.6785714285) = 0.1747448979

Calculate the square root of the right side: 0.418024997

Break this problem into two subproblems by setting 
(n + 0.6785714285) equal to 0.418024997 and -0.418024997.

Subproblem 1
n + 0.6785714285 = 0.418024997

Simplifying
n + 0.6785714285 = 0.418024997

Reorder the terms:
0.6785714285 + n = 0.418024997

Solving
0.6785714285 + n = 0.418024997

Solving for variable 'n'.

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

Add '-0.6785714285' to each side of the equation.
0.6785714285 + -0.6785714285 + n = 0.418024997 + -0.6785714285

Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000
0.0000000000 + n = 0.418024997 + -0.6785714285
n = 0.418024997 + -0.6785714285

Combine like terms: 0.418024997 + -0.6785714285 = -0.2605464315
n = -0.2605464315

Simplifying
n = -0.2605464315

Subproblem 2
n + 0.6785714285 = -0.418024997

Simplifying
n + 0.6785714285 = -0.418024997

Reorder the terms:
0.6785714285 + n = -0.418024997

Solving
0.6785714285 + n = -0.418024997

Solving for variable 'n'.

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

Add '-0.6785714285' to each side of the equation.
0.6785714285 + -0.6785714285 + n = -0.418024997 + -0.6785714285

Combine like terms: 0.6785714285 + -0.6785714285 = 0.0000000000
0.0000000000 + n = -0.418024997 + -0.6785714285
n = -0.418024997 + -0.6785714285

Combine like terms: -0.418024997 + -0.6785714285 = -1.0965964255
n = -1.0965964255

Simplifying
n = -1.0965964255

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {-0.2605464315, -1.0965964255}