5n+7=7(n+1)2n

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

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

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

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

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

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

Solving
7 + 5n = 14n + 14n2

Solving for variable 'n'.

Combine like terms: 5n + -14n = -9n
7 + -9n + -14n2 = 14n + 14n2 + -14n + -14n2

Reorder the terms:
7 + -9n + -14n2 = 14n + -14n + 14n2 + -14n2

Combine like terms: 14n + -14n = 0
7 + -9n + -14n2 = 0 + 14n2 + -14n2
7 + -9n + -14n2 = 14n2 + -14n2

Combine like terms: 14n2 + -14n2 = 0
7 + -9n + -14n2 = 0

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

Divide each side by '-14'.
-0.5 + 0.6428571429n + n2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.6428571429n + 0.5 + n2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.6428571429n + n2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.6428571429n + n2 = 0 + 0.5
0.6428571429n + n2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.6428571429n + n2 = 0.5

The n term is 0.6428571429n.  Take half its coefficient (0.3214285715).
Square it (0.1033163266) and add it to both sides.

Add '0.1033163266' to each side of the equation.
0.6428571429n + 0.1033163266 + n2 = 0.5 + 0.1033163266

Reorder the terms:
0.1033163266 + 0.6428571429n + n2 = 0.5 + 0.1033163266

Combine like terms: 0.5 + 0.1033163266 = 0.6033163266
0.1033163266 + 0.6428571429n + n2 = 0.6033163266

Factor a perfect square on the left side:
(n + 0.3214285715)(n + 0.3214285715) = 0.6033163266

Calculate the square root of the right side: 0.776734399

Break this problem into two subproblems by setting 
(n + 0.3214285715) equal to 0.776734399 and -0.776734399.

Subproblem 1
n + 0.3214285715 = 0.776734399

Simplifying
n + 0.3214285715 = 0.776734399

Reorder the terms:
0.3214285715 + n = 0.776734399

Solving
0.3214285715 + n = 0.776734399

Solving for variable 'n'.

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

Add '-0.3214285715' to each side of the equation.
0.3214285715 + -0.3214285715 + n = 0.776734399 + -0.3214285715

Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000
0.0000000000 + n = 0.776734399 + -0.3214285715
n = 0.776734399 + -0.3214285715

Combine like terms: 0.776734399 + -0.3214285715 = 0.4553058275
n = 0.4553058275

Simplifying
n = 0.4553058275

Subproblem 2
n + 0.3214285715 = -0.776734399

Simplifying
n + 0.3214285715 = -0.776734399

Reorder the terms:
0.3214285715 + n = -0.776734399

Solving
0.3214285715 + n = -0.776734399

Solving for variable 'n'.

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

Add '-0.3214285715' to each side of the equation.
0.3214285715 + -0.3214285715 + n = -0.776734399 + -0.3214285715

Combine like terms: 0.3214285715 + -0.3214285715 = 0.0000000000
0.0000000000 + n = -0.776734399 + -0.3214285715
n = -0.776734399 + -0.3214285715

Combine like terms: -0.776734399 + -0.3214285715 = -1.0981629705
n = -1.0981629705

Simplifying
n = -1.0981629705

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.4553058275, -1.0981629705}