(7x+x)(x)=(x+3)(x+3)

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

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

Combine like terms: 7x + x = 8x
(8x)(x) = (x + 3)(x + 3)

Remove parenthesis around (8x)
8x(x) = (x + 3)(x + 3)

Multiply x * x
8x2 = (x + 3)(x + 3)

Reorder the terms:
8x2 = (3 + x)(x + 3)

Reorder the terms:
8x2 = (3 + x)(3 + x)

Multiply (3 + x) * (3 + x)
8x2 = (3(3 + x) + x(3 + x))
8x2 = ((3 * 3 + x * 3) + x(3 + x))
8x2 = ((9 + 3x) + x(3 + x))
8x2 = (9 + 3x + (3 * x + x * x))
8x2 = (9 + 3x + (3x + x2))

Combine like terms: 3x + 3x = 6x
8x2 = (9 + 6x + x2)

Solving
8x2 = 9 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-9 + -6x + 8x2 + -1x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Combine like terms: 8x2 + -1x2 = 7x2
-9 + -6x + 7x2 = 9 + 6x + x2 + -9 + -6x + -1x2

Reorder the terms:
-9 + -6x + 7x2 = 9 + -9 + 6x + -6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-9 + -6x + 7x2 = 0 + 6x + -6x + x2 + -1x2
-9 + -6x + 7x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-9 + -6x + 7x2 = 0 + x2 + -1x2
-9 + -6x + 7x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-9 + -6x + 7x2 = 0

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

Divide each side by '7'.
-1.285714286 + -0.8571428571x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + -0.8571428571x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + -0.8571428571x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + -0.8571428571x + x2 = 0 + 1.285714286
-0.8571428571x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
-0.8571428571x + x2 = 1.285714286

The x term is -0.8571428571x.  Take half its coefficient (-0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
-0.8571428571x + 0.1836734694 + x2 = 1.285714286 + 0.1836734694

Reorder the terms:
0.1836734694 + -0.8571428571x + x2 = 1.285714286 + 0.1836734694

Combine like terms: 1.285714286 + 0.1836734694 = 1.4693877554
0.1836734694 + -0.8571428571x + x2 = 1.4693877554

Factor a perfect square on the left side:
(x + -0.4285714286)(x + -0.4285714286) = 1.4693877554

Calculate the square root of the right side: 1.212183054

Break this problem into two subproblems by setting 
(x + -0.4285714286) equal to 1.212183054 and -1.212183054.

Subproblem 1
x + -0.4285714286 = 1.212183054

Simplifying
x + -0.4285714286 = 1.212183054

Reorder the terms:
-0.4285714286 + x = 1.212183054

Solving
-0.4285714286 + x = 1.212183054

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = 1.212183054 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = 1.212183054 + 0.4285714286
x = 1.212183054 + 0.4285714286

Combine like terms: 1.212183054 + 0.4285714286 = 1.6407544826
x = 1.6407544826

Simplifying
x = 1.6407544826

Subproblem 2
x + -0.4285714286 = -1.212183054

Simplifying
x + -0.4285714286 = -1.212183054

Reorder the terms:
-0.4285714286 + x = -1.212183054

Solving
-0.4285714286 + x = -1.212183054

Solving for variable 'x'.

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

Add '0.4285714286' to each side of the equation.
-0.4285714286 + 0.4285714286 + x = -1.212183054 + 0.4285714286

Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000
0.0000000000 + x = -1.212183054 + 0.4285714286
x = -1.212183054 + 0.4285714286

Combine like terms: -1.212183054 + 0.4285714286 = -0.7836116254
x = -0.7836116254

Simplifying
x = -0.7836116254

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6407544826, -0.7836116254}