3(2x+1)+3(x+1)=5(2x+1)(x+1)

Solution for 3(2x+1)+3(x+1)=5(2x+1)(x+1) equation:

Simplifying
3(2x + 1) + 3(x + 1) = 5(2x + 1)(x + 1)

Reorder the terms:
3(1 + 2x) + 3(x + 1) = 5(2x + 1)(x + 1)
(1 * 3 + 2x * 3) + 3(x + 1) = 5(2x + 1)(x + 1)
(3 + 6x) + 3(x + 1) = 5(2x + 1)(x + 1)

Reorder the terms:
3 + 6x + 3(1 + x) = 5(2x + 1)(x + 1)
3 + 6x + (1 * 3 + x * 3) = 5(2x + 1)(x + 1)
3 + 6x + (3 + 3x) = 5(2x + 1)(x + 1)

Reorder the terms:
3 + 3 + 6x + 3x = 5(2x + 1)(x + 1)

Combine like terms: 3 + 3 = 6
6 + 6x + 3x = 5(2x + 1)(x + 1)

Combine like terms: 6x + 3x = 9x
6 + 9x = 5(2x + 1)(x + 1)

Reorder the terms:
6 + 9x = 5(1 + 2x)(x + 1)

Reorder the terms:
6 + 9x = 5(1 + 2x)(1 + x)

Multiply (1 + 2x) * (1 + x)
6 + 9x = 5(1(1 + x) + 2x * (1 + x))
6 + 9x = 5((1 * 1 + x * 1) + 2x * (1 + x))
6 + 9x = 5((1 + 1x) + 2x * (1 + x))
6 + 9x = 5(1 + 1x + (1 * 2x + x * 2x))
6 + 9x = 5(1 + 1x + (2x + 2x2))

Combine like terms: 1x + 2x = 3x
6 + 9x = 5(1 + 3x + 2x2)
6 + 9x = (1 * 5 + 3x * 5 + 2x2 * 5)
6 + 9x = (5 + 15x + 10x2)

Solving
6 + 9x = 5 + 15x + 10x2

Solving for variable 'x'.

Reorder the terms:
6 + -5 + 9x + -15x + -10x2 = 5 + 15x + 10x2 + -5 + -15x + -10x2

Combine like terms: 6 + -5 = 1
1 + 9x + -15x + -10x2 = 5 + 15x + 10x2 + -5 + -15x + -10x2

Combine like terms: 9x + -15x = -6x
1 + -6x + -10x2 = 5 + 15x + 10x2 + -5 + -15x + -10x2

Reorder the terms:
1 + -6x + -10x2 = 5 + -5 + 15x + -15x + 10x2 + -10x2

Combine like terms: 5 + -5 = 0
1 + -6x + -10x2 = 0 + 15x + -15x + 10x2 + -10x2
1 + -6x + -10x2 = 15x + -15x + 10x2 + -10x2

Combine like terms: 15x + -15x = 0
1 + -6x + -10x2 = 0 + 10x2 + -10x2
1 + -6x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
1 + -6x + -10x2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.1 + 0.6x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + 0.6x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + 0.6x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + 0.6x + x2 = 0 + 0.1
0.6x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
0.6x + x2 = 0.1

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 0.1 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 0.1 + 0.09

Combine like terms: 0.1 + 0.09 = 0.19
0.09 + 0.6x + x2 = 0.19

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 0.19

Calculate the square root of the right side: 0.435889894

Break this problem into two subproblems by setting 
(x + 0.3) equal to 0.435889894 and -0.435889894.

Subproblem 1
x + 0.3 = 0.435889894

Simplifying
x + 0.3 = 0.435889894

Reorder the terms:
0.3 + x = 0.435889894

Solving
0.3 + x = 0.435889894

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 0.435889894 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 0.435889894 + -0.3
x = 0.435889894 + -0.3

Combine like terms: 0.435889894 + -0.3 = 0.135889894
x = 0.135889894

Simplifying
x = 0.135889894

Subproblem 2
x + 0.3 = -0.435889894

Simplifying
x + 0.3 = -0.435889894

Reorder the terms:
0.3 + x = -0.435889894

Solving
0.3 + x = -0.435889894

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -0.435889894 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -0.435889894 + -0.3
x = -0.435889894 + -0.3

Combine like terms: -0.435889894 + -0.3 = -0.735889894
x = -0.735889894

Simplifying
x = -0.735889894

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.135889894, -0.735889894}