(x+7)(7x-1)=x+3

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

Simplifying
(x + 7)(7x + -1) = x + 3

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

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

Multiply (7 + x) * (-1 + 7x)
(7(-1 + 7x) + x(-1 + 7x)) = x + 3
((-1 * 7 + 7x * 7) + x(-1 + 7x)) = x + 3
((-7 + 49x) + x(-1 + 7x)) = x + 3
(-7 + 49x + (-1 * x + 7x * x)) = x + 3
(-7 + 49x + (-1x + 7x2)) = x + 3

Combine like terms: 49x + -1x = 48x
(-7 + 48x + 7x2) = x + 3

Reorder the terms:
-7 + 48x + 7x2 = 3 + x

Solving
-7 + 48x + 7x2 = 3 + x

Solving for variable 'x'.

Reorder the terms:
-7 + -3 + 48x + -1x + 7x2 = 3 + x + -3 + -1x

Combine like terms: -7 + -3 = -10
-10 + 48x + -1x + 7x2 = 3 + x + -3 + -1x

Combine like terms: 48x + -1x = 47x
-10 + 47x + 7x2 = 3 + x + -3 + -1x

Reorder the terms:
-10 + 47x + 7x2 = 3 + -3 + x + -1x

Combine like terms: 3 + -3 = 0
-10 + 47x + 7x2 = 0 + x + -1x
-10 + 47x + 7x2 = x + -1x

Combine like terms: x + -1x = 0
-10 + 47x + 7x2 = 0

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

Divide each side by '7'.
-1.428571429 + 6.714285714x + x2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + 6.714285714x + 1.428571429 + x2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + 6.714285714x + x2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + 6.714285714x + x2 = 0 + 1.428571429
6.714285714x + x2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
6.714285714x + x2 = 1.428571429

The x term is 6.714285714x.  Take half its coefficient (3.357142857).
Square it (11.27040816) and add it to both sides.

Add '11.27040816' to each side of the equation.
6.714285714x + 11.27040816 + x2 = 1.428571429 + 11.27040816

Reorder the terms:
11.27040816 + 6.714285714x + x2 = 1.428571429 + 11.27040816

Combine like terms: 1.428571429 + 11.27040816 = 12.698979589
11.27040816 + 6.714285714x + x2 = 12.698979589

Factor a perfect square on the left side:
(x + 3.357142857)(x + 3.357142857) = 12.698979589

Calculate the square root of the right side: 3.563562766

Break this problem into two subproblems by setting 
(x + 3.357142857) equal to 3.563562766 and -3.563562766.

Subproblem 1
x + 3.357142857 = 3.563562766

Simplifying
x + 3.357142857 = 3.563562766

Reorder the terms:
3.357142857 + x = 3.563562766

Solving
3.357142857 + x = 3.563562766

Solving for variable 'x'.

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

Add '-3.357142857' to each side of the equation.
3.357142857 + -3.357142857 + x = 3.563562766 + -3.357142857

Combine like terms: 3.357142857 + -3.357142857 = 0.000000000
0.000000000 + x = 3.563562766 + -3.357142857
x = 3.563562766 + -3.357142857

Combine like terms: 3.563562766 + -3.357142857 = 0.206419909
x = 0.206419909

Simplifying
x = 0.206419909

Subproblem 2
x + 3.357142857 = -3.563562766

Simplifying
x + 3.357142857 = -3.563562766

Reorder the terms:
3.357142857 + x = -3.563562766

Solving
3.357142857 + x = -3.563562766

Solving for variable 'x'.

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

Add '-3.357142857' to each side of the equation.
3.357142857 + -3.357142857 + x = -3.563562766 + -3.357142857

Combine like terms: 3.357142857 + -3.357142857 = 0.000000000
0.000000000 + x = -3.563562766 + -3.357142857
x = -3.563562766 + -3.357142857

Combine like terms: -3.563562766 + -3.357142857 = -6.920705623
x = -6.920705623

Simplifying
x = -6.920705623

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.206419909, -6.920705623}