(3x+7)(3x-1)=(2x+5)(x)

Solution for (3x+7)(3x-1)=(2x+5)(x) equation:

Simplifying
(3x + 7)(3x + -1) = (2x + 5)(x)

Reorder the terms:
(7 + 3x)(3x + -1) = (2x + 5)(x)

Reorder the terms:
(7 + 3x)(-1 + 3x) = (2x + 5)(x)

Multiply (7 + 3x) * (-1 + 3x)
(7(-1 + 3x) + 3x * (-1 + 3x)) = (2x + 5)(x)
((-1 * 7 + 3x * 7) + 3x * (-1 + 3x)) = (2x + 5)(x)
((-7 + 21x) + 3x * (-1 + 3x)) = (2x + 5)(x)
(-7 + 21x + (-1 * 3x + 3x * 3x)) = (2x + 5)(x)
(-7 + 21x + (-3x + 9x2)) = (2x + 5)(x)

Combine like terms: 21x + -3x = 18x
(-7 + 18x + 9x2) = (2x + 5)(x)

Reorder the terms:
-7 + 18x + 9x2 = (5 + 2x)(x)

Reorder the terms for easier multiplication:
-7 + 18x + 9x2 = x(5 + 2x)
-7 + 18x + 9x2 = (5 * x + 2x * x)
-7 + 18x + 9x2 = (5x + 2x2)

Solving
-7 + 18x + 9x2 = 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-7 + 18x + -5x + 9x2 + -2x2 = 5x + 2x2 + -5x + -2x2

Combine like terms: 18x + -5x = 13x
-7 + 13x + 9x2 + -2x2 = 5x + 2x2 + -5x + -2x2

Combine like terms: 9x2 + -2x2 = 7x2
-7 + 13x + 7x2 = 5x + 2x2 + -5x + -2x2

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

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

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

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

Divide each side by '7'.
-1 + 1.857142857x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.857142857x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.857142857x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.857142857x + x2 = 0 + 1
1.857142857x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.857142857x + x2 = 1

The x term is 1.857142857x.  Take half its coefficient (0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
1.857142857x + 0.8622448978 + x2 = 1 + 0.8622448978

Reorder the terms:
0.8622448978 + 1.857142857x + x2 = 1 + 0.8622448978

Combine like terms: 1 + 0.8622448978 = 1.8622448978
0.8622448978 + 1.857142857x + x2 = 1.8622448978

Factor a perfect square on the left side:
(x + 0.9285714285)(x + 0.9285714285) = 1.8622448978

Calculate the square root of the right side: 1.364640941

Break this problem into two subproblems by setting 
(x + 0.9285714285) equal to 1.364640941 and -1.364640941.

Subproblem 1
x + 0.9285714285 = 1.364640941

Simplifying
x + 0.9285714285 = 1.364640941

Reorder the terms:
0.9285714285 + x = 1.364640941

Solving
0.9285714285 + x = 1.364640941

Solving for variable 'x'.

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

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + x = 1.364640941 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + x = 1.364640941 + -0.9285714285
x = 1.364640941 + -0.9285714285

Combine like terms: 1.364640941 + -0.9285714285 = 0.4360695125
x = 0.4360695125

Simplifying
x = 0.4360695125

Subproblem 2
x + 0.9285714285 = -1.364640941

Simplifying
x + 0.9285714285 = -1.364640941

Reorder the terms:
0.9285714285 + x = -1.364640941

Solving
0.9285714285 + x = -1.364640941

Solving for variable 'x'.

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

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + x = -1.364640941 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + x = -1.364640941 + -0.9285714285
x = -1.364640941 + -0.9285714285

Combine like terms: -1.364640941 + -0.9285714285 = -2.2932123695
x = -2.2932123695

Simplifying
x = -2.2932123695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4360695125, -2.2932123695}