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

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

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

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

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

Multiply (5 + 2x) * (1 + 2x)
(5(1 + 2x) + 2x * (1 + 2x)) = 3(x + 1)(x + 1)
((1 * 5 + 2x * 5) + 2x * (1 + 2x)) = 3(x + 1)(x + 1)
((5 + 10x) + 2x * (1 + 2x)) = 3(x + 1)(x + 1)
(5 + 10x + (1 * 2x + 2x * 2x)) = 3(x + 1)(x + 1)
(5 + 10x + (2x + 4x2)) = 3(x + 1)(x + 1)

Combine like terms: 10x + 2x = 12x
(5 + 12x + 4x2) = 3(x + 1)(x + 1)

Reorder the terms:
5 + 12x + 4x2 = 3(1 + x)(x + 1)

Reorder the terms:
5 + 12x + 4x2 = 3(1 + x)(1 + x)

Multiply (1 + x) * (1 + x)
5 + 12x + 4x2 = 3(1(1 + x) + x(1 + x))
5 + 12x + 4x2 = 3((1 * 1 + x * 1) + x(1 + x))
5 + 12x + 4x2 = 3((1 + 1x) + x(1 + x))
5 + 12x + 4x2 = 3(1 + 1x + (1 * x + x * x))
5 + 12x + 4x2 = 3(1 + 1x + (1x + x2))

Combine like terms: 1x + 1x = 2x
5 + 12x + 4x2 = 3(1 + 2x + x2)
5 + 12x + 4x2 = (1 * 3 + 2x * 3 + x2 * 3)
5 + 12x + 4x2 = (3 + 6x + 3x2)

Solving
5 + 12x + 4x2 = 3 + 6x + 3x2

Solving for variable 'x'.

Reorder the terms:
5 + -3 + 12x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: 5 + -3 = 2
2 + 12x + -6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: 12x + -6x = 6x
2 + 6x + 4x2 + -3x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Combine like terms: 4x2 + -3x2 = 1x2
2 + 6x + 1x2 = 3 + 6x + 3x2 + -3 + -6x + -3x2

Reorder the terms:
2 + 6x + 1x2 = 3 + -3 + 6x + -6x + 3x2 + -3x2

Combine like terms: 3 + -3 = 0
2 + 6x + 1x2 = 0 + 6x + -6x + 3x2 + -3x2
2 + 6x + 1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
2 + 6x + 1x2 = 0 + 3x2 + -3x2
2 + 6x + 1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
2 + 6x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 6x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 6x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 6x + x2 = 0 + -2
6x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
6x + x2 = -2

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -2 + 9

Reorder the terms:
9 + 6x + x2 = -2 + 9

Combine like terms: -2 + 9 = 7
9 + 6x + x2 = 7

Factor a perfect square on the left side:
(x + 3)(x + 3) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(x + 3) equal to 2.645751311 and -2.645751311.

Subproblem 1
x + 3 = 2.645751311

Simplifying
x + 3 = 2.645751311

Reorder the terms:
3 + x = 2.645751311

Solving
3 + x = 2.645751311

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + x = 2.645751311 + -3
x = 2.645751311 + -3

Combine like terms: 2.645751311 + -3 = -0.354248689
x = -0.354248689

Simplifying
x = -0.354248689

Subproblem 2
x + 3 = -2.645751311

Simplifying
x + 3 = -2.645751311

Reorder the terms:
3 + x = -2.645751311

Solving
3 + x = -2.645751311

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -2.645751311 + -3

Combine like terms: 3 + -3 = 0
0 + x = -2.645751311 + -3
x = -2.645751311 + -3

Combine like terms: -2.645751311 + -3 = -5.645751311
x = -5.645751311

Simplifying
x = -5.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.354248689, -5.645751311}