(20x+2)(15x+3)=x

Solution for (20x+2)(15x+3)=x equation:

Simplifying
(20x + 2)(15x + 3) = x

Reorder the terms:
(2 + 20x)(15x + 3) = x

Reorder the terms:
(2 + 20x)(3 + 15x) = x

Multiply (2 + 20x) * (3 + 15x)
(2(3 + 15x) + 20x * (3 + 15x)) = x
((3 * 2 + 15x * 2) + 20x * (3 + 15x)) = x
((6 + 30x) + 20x * (3 + 15x)) = x
(6 + 30x + (3 * 20x + 15x * 20x)) = x
(6 + 30x + (60x + 300x2)) = x

Combine like terms: 30x + 60x = 90x
(6 + 90x + 300x2) = x

Solving
6 + 90x + 300x2 = x

Solving for variable 'x'.

Reorder the terms:
6 + 90x + -1x + 300x2 = x + -1x

Combine like terms: 90x + -1x = 89x
6 + 89x + 300x2 = x + -1x

Combine like terms: x + -1x = 0
6 + 89x + 300x2 = 0

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

Divide each side by '300'.
0.02 + 0.2966666667x + x2 = 0.00

Move the constant term to the right:

Add '-0.02' to each side of the equation.
0.02 + 0.2966666667x + -0.02 + x2 = 0.00 + -0.02

Reorder the terms:
0.02 + -0.02 + 0.2966666667x + x2 = 0.00 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + 0.2966666667x + x2 = 0.00 + -0.02
0.2966666667x + x2 = 0.00 + -0.02

Combine like terms: 0.00 + -0.02 = -0.02
0.2966666667x + x2 = -0.02

The x term is 0.2966666667x.  Take half its coefficient (0.1483333334).
Square it (0.02200277780) and add it to both sides.

Add '0.02200277780' to each side of the equation.
0.2966666667x + 0.02200277780 + x2 = -0.02 + 0.02200277780

Reorder the terms:
0.02200277780 + 0.2966666667x + x2 = -0.02 + 0.02200277780

Combine like terms: -0.02 + 0.02200277780 = 0.0020027778
0.02200277780 + 0.2966666667x + x2 = 0.0020027778

Factor a perfect square on the left side:
(x + 0.1483333334)(x + 0.1483333334) = 0.0020027778

Calculate the square root of the right side: 0.044752406

Break this problem into two subproblems by setting 
(x + 0.1483333334) equal to 0.044752406 and -0.044752406.

Subproblem 1
x + 0.1483333334 = 0.044752406

Simplifying
x + 0.1483333334 = 0.044752406

Reorder the terms:
0.1483333334 + x = 0.044752406

Solving
0.1483333334 + x = 0.044752406

Solving for variable 'x'.

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

Add '-0.1483333334' to each side of the equation.
0.1483333334 + -0.1483333334 + x = 0.044752406 + -0.1483333334

Combine like terms: 0.1483333334 + -0.1483333334 = 0.0000000000
0.0000000000 + x = 0.044752406 + -0.1483333334
x = 0.044752406 + -0.1483333334

Combine like terms: 0.044752406 + -0.1483333334 = -0.1035809274
x = -0.1035809274

Simplifying
x = -0.1035809274

Subproblem 2
x + 0.1483333334 = -0.044752406

Simplifying
x + 0.1483333334 = -0.044752406

Reorder the terms:
0.1483333334 + x = -0.044752406

Solving
0.1483333334 + x = -0.044752406

Solving for variable 'x'.

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

Add '-0.1483333334' to each side of the equation.
0.1483333334 + -0.1483333334 + x = -0.044752406 + -0.1483333334

Combine like terms: 0.1483333334 + -0.1483333334 = 0.0000000000
0.0000000000 + x = -0.044752406 + -0.1483333334
x = -0.044752406 + -0.1483333334

Combine like terms: -0.044752406 + -0.1483333334 = -0.1930857394
x = -0.1930857394

Simplifying
x = -0.1930857394

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1035809274, -0.1930857394}