(6x+3)(x+5)=(2+x)(6+2x)-4

Solution for (6x+3)(x+5)=(2+x)(6+2x)-4 equation:

Simplifying
(6x + 3)(x + 5) = (2 + x)(6 + 2x) + -4

Reorder the terms:
(3 + 6x)(x + 5) = (2 + x)(6 + 2x) + -4

Reorder the terms:
(3 + 6x)(5 + x) = (2 + x)(6 + 2x) + -4

Multiply (3 + 6x) * (5 + x)
(3(5 + x) + 6x * (5 + x)) = (2 + x)(6 + 2x) + -4
((5 * 3 + x * 3) + 6x * (5 + x)) = (2 + x)(6 + 2x) + -4
((15 + 3x) + 6x * (5 + x)) = (2 + x)(6 + 2x) + -4
(15 + 3x + (5 * 6x + x * 6x)) = (2 + x)(6 + 2x) + -4
(15 + 3x + (30x + 6x2)) = (2 + x)(6 + 2x) + -4

Combine like terms: 3x + 30x = 33x
(15 + 33x + 6x2) = (2 + x)(6 + 2x) + -4

Multiply (2 + x) * (6 + 2x)
15 + 33x + 6x2 = (2(6 + 2x) + x(6 + 2x)) + -4
15 + 33x + 6x2 = ((6 * 2 + 2x * 2) + x(6 + 2x)) + -4
15 + 33x + 6x2 = ((12 + 4x) + x(6 + 2x)) + -4
15 + 33x + 6x2 = (12 + 4x + (6 * x + 2x * x)) + -4
15 + 33x + 6x2 = (12 + 4x + (6x + 2x2)) + -4

Combine like terms: 4x + 6x = 10x
15 + 33x + 6x2 = (12 + 10x + 2x2) + -4

Reorder the terms:
15 + 33x + 6x2 = 12 + -4 + 10x + 2x2

Combine like terms: 12 + -4 = 8
15 + 33x + 6x2 = 8 + 10x + 2x2

Solving
15 + 33x + 6x2 = 8 + 10x + 2x2

Solving for variable 'x'.

Reorder the terms:
15 + -8 + 33x + -10x + 6x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 15 + -8 = 7
7 + 33x + -10x + 6x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 33x + -10x = 23x
7 + 23x + 6x2 + -2x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Combine like terms: 6x2 + -2x2 = 4x2
7 + 23x + 4x2 = 8 + 10x + 2x2 + -8 + -10x + -2x2

Reorder the terms:
7 + 23x + 4x2 = 8 + -8 + 10x + -10x + 2x2 + -2x2

Combine like terms: 8 + -8 = 0
7 + 23x + 4x2 = 0 + 10x + -10x + 2x2 + -2x2
7 + 23x + 4x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
7 + 23x + 4x2 = 0 + 2x2 + -2x2
7 + 23x + 4x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
7 + 23x + 4x2 = 0

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

Divide each side by '4'.
1.75 + 5.75x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 5.75x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 5.75x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 5.75x + x2 = 0 + -1.75
5.75x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
5.75x + x2 = -1.75

The x term is 5.75x.  Take half its coefficient (2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
5.75x + 8.265625 + x2 = -1.75 + 8.265625

Reorder the terms:
8.265625 + 5.75x + x2 = -1.75 + 8.265625

Combine like terms: -1.75 + 8.265625 = 6.515625
8.265625 + 5.75x + x2 = 6.515625

Factor a perfect square on the left side:
(x + 2.875)(x + 2.875) = 6.515625

Calculate the square root of the right side: 2.552572232

Break this problem into two subproblems by setting 
(x + 2.875) equal to 2.552572232 and -2.552572232.

Subproblem 1
x + 2.875 = 2.552572232

Simplifying
x + 2.875 = 2.552572232

Reorder the terms:
2.875 + x = 2.552572232

Solving
2.875 + x = 2.552572232

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = 2.552572232 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = 2.552572232 + -2.875
x = 2.552572232 + -2.875

Combine like terms: 2.552572232 + -2.875 = -0.322427768
x = -0.322427768

Simplifying
x = -0.322427768

Subproblem 2
x + 2.875 = -2.552572232

Simplifying
x + 2.875 = -2.552572232

Reorder the terms:
2.875 + x = -2.552572232

Solving
2.875 + x = -2.552572232

Solving for variable 'x'.

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

Add '-2.875' to each side of the equation.
2.875 + -2.875 + x = -2.552572232 + -2.875

Combine like terms: 2.875 + -2.875 = 0.000
0.000 + x = -2.552572232 + -2.875
x = -2.552572232 + -2.875

Combine like terms: -2.552572232 + -2.875 = -5.427572232
x = -5.427572232

Simplifying
x = -5.427572232

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.322427768, -5.427572232}