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

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

Simplifying
3x(2 + 5x) = (2x + 5)(x + 1)
(2 * 3x + 5x * 3x) = (2x + 5)(x + 1)
(6x + 15x2) = (2x + 5)(x + 1)

Reorder the terms:
6x + 15x2 = (5 + 2x)(x + 1)

Reorder the terms:
6x + 15x2 = (5 + 2x)(1 + x)

Multiply (5 + 2x) * (1 + x)
6x + 15x2 = (5(1 + x) + 2x * (1 + x))
6x + 15x2 = ((1 * 5 + x * 5) + 2x * (1 + x))
6x + 15x2 = ((5 + 5x) + 2x * (1 + x))
6x + 15x2 = (5 + 5x + (1 * 2x + x * 2x))
6x + 15x2 = (5 + 5x + (2x + 2x2))

Combine like terms: 5x + 2x = 7x
6x + 15x2 = (5 + 7x + 2x2)

Solving
6x + 15x2 = 5 + 7x + 2x2

Solving for variable 'x'.

Reorder the terms:
-5 + 6x + -7x + 15x2 + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Combine like terms: 6x + -7x = -1x
-5 + -1x + 15x2 + -2x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Combine like terms: 15x2 + -2x2 = 13x2
-5 + -1x + 13x2 = 5 + 7x + 2x2 + -5 + -7x + -2x2

Reorder the terms:
-5 + -1x + 13x2 = 5 + -5 + 7x + -7x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-5 + -1x + 13x2 = 0 + 7x + -7x + 2x2 + -2x2
-5 + -1x + 13x2 = 7x + -7x + 2x2 + -2x2

Combine like terms: 7x + -7x = 0
-5 + -1x + 13x2 = 0 + 2x2 + -2x2
-5 + -1x + 13x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + -1x + 13x2 = 0

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

Divide each side by '13'.
-0.3846153846 + -0.07692307692x + x2 = 0

Move the constant term to the right:

Add '0.3846153846' to each side of the equation.
-0.3846153846 + -0.07692307692x + 0.3846153846 + x2 = 0 + 0.3846153846

Reorder the terms:
-0.3846153846 + 0.3846153846 + -0.07692307692x + x2 = 0 + 0.3846153846

Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000
0.0000000000 + -0.07692307692x + x2 = 0 + 0.3846153846
-0.07692307692x + x2 = 0 + 0.3846153846

Combine like terms: 0 + 0.3846153846 = 0.3846153846
-0.07692307692x + x2 = 0.3846153846

The x term is -0.07692307692x.  Take half its coefficient (-0.03846153846).
Square it (0.001479289941) and add it to both sides.

Add '0.001479289941' to each side of the equation.
-0.07692307692x + 0.001479289941 + x2 = 0.3846153846 + 0.001479289941

Reorder the terms:
0.001479289941 + -0.07692307692x + x2 = 0.3846153846 + 0.001479289941

Combine like terms: 0.3846153846 + 0.001479289941 = 0.386094674541
0.001479289941 + -0.07692307692x + x2 = 0.386094674541

Factor a perfect square on the left side:
(x + -0.03846153846)(x + -0.03846153846) = 0.386094674541

Calculate the square root of the right side: 0.62136517

Break this problem into two subproblems by setting 
(x + -0.03846153846) equal to 0.62136517 and -0.62136517.

Subproblem 1
x + -0.03846153846 = 0.62136517

Simplifying
x + -0.03846153846 = 0.62136517

Reorder the terms:
-0.03846153846 + x = 0.62136517

Solving
-0.03846153846 + x = 0.62136517

Solving for variable 'x'.

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

Add '0.03846153846' to each side of the equation.
-0.03846153846 + 0.03846153846 + x = 0.62136517 + 0.03846153846

Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000
0.00000000000 + x = 0.62136517 + 0.03846153846
x = 0.62136517 + 0.03846153846

Combine like terms: 0.62136517 + 0.03846153846 = 0.65982670846
x = 0.65982670846

Simplifying
x = 0.65982670846

Subproblem 2
x + -0.03846153846 = -0.62136517

Simplifying
x + -0.03846153846 = -0.62136517

Reorder the terms:
-0.03846153846 + x = -0.62136517

Solving
-0.03846153846 + x = -0.62136517

Solving for variable 'x'.

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

Add '0.03846153846' to each side of the equation.
-0.03846153846 + 0.03846153846 + x = -0.62136517 + 0.03846153846

Combine like terms: -0.03846153846 + 0.03846153846 = 0.00000000000
0.00000000000 + x = -0.62136517 + 0.03846153846
x = -0.62136517 + 0.03846153846

Combine like terms: -0.62136517 + 0.03846153846 = -0.58290363154
x = -0.58290363154

Simplifying
x = -0.58290363154

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.65982670846, -0.58290363154}