300x-4=20x(23)(3x)

Solution for 300x-4=20x(23)(3x) equation:

Simplifying
300x + -4 = 20x(23)(3x)

Reorder the terms:
-4 + 300x = 20x(23)(3x)

Remove parenthesis around (3x)
-4 + 300x = 20x * 23 * 3x

Reorder the terms for easier multiplication:
-4 + 300x = 20 * 23 * 3x * x

Multiply 20 * 23
-4 + 300x = 460 * 3x * x

Multiply 460 * 3
-4 + 300x = 1380x * x

Multiply x * x
-4 + 300x = 1380x2

Solving
-4 + 300x = 1380x2

Solving for variable 'x'.

Combine like terms: 1380x2 + -1380x2 = 0
-4 + 300x + -1380x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + 75x + -345x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + 75x + -345x2)' equal to zero and attempt to solve:

Simplifying
-1 + 75x + -345x2 = 0

Solving
-1 + 75x + -345x2 = 0

Begin completing the square.  Divide all terms by
-345 the coefficient of the squared term: 

Divide each side by '-345'.
0.002898550725 + -0.2173913043x + x2 = 0

Move the constant term to the right:

Add '-0.002898550725' to each side of the equation.
0.002898550725 + -0.2173913043x + -0.002898550725 + x2 = 0 + -0.002898550725

Reorder the terms:
0.002898550725 + -0.002898550725 + -0.2173913043x + x2 = 0 + -0.002898550725

Combine like terms: 0.002898550725 + -0.002898550725 = 0.000000000000
0.000000000000 + -0.2173913043x + x2 = 0 + -0.002898550725
-0.2173913043x + x2 = 0 + -0.002898550725

Combine like terms: 0 + -0.002898550725 = -0.002898550725
-0.2173913043x + x2 = -0.002898550725

The x term is -0.2173913043x.  Take half its coefficient (-0.1086956522).
Square it (0.01181474481) and add it to both sides.

Add '0.01181474481' to each side of the equation.
-0.2173913043x + 0.01181474481 + x2 = -0.002898550725 + 0.01181474481

Reorder the terms:
0.01181474481 + -0.2173913043x + x2 = -0.002898550725 + 0.01181474481

Combine like terms: -0.002898550725 + 0.01181474481 = 0.008916194085
0.01181474481 + -0.2173913043x + x2 = 0.008916194085

Factor a perfect square on the left side:
(x + -0.1086956522)(x + -0.1086956522) = 0.008916194085

Calculate the square root of the right side: 0.094425601

Break this problem into two subproblems by setting 
(x + -0.1086956522) equal to 0.094425601 and -0.094425601.

Subproblem 1
x + -0.1086956522 = 0.094425601

Simplifying
x + -0.1086956522 = 0.094425601

Reorder the terms:
-0.1086956522 + x = 0.094425601

Solving
-0.1086956522 + x = 0.094425601

Solving for variable 'x'.

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

Add '0.1086956522' to each side of the equation.
-0.1086956522 + 0.1086956522 + x = 0.094425601 + 0.1086956522

Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000
0.0000000000 + x = 0.094425601 + 0.1086956522
x = 0.094425601 + 0.1086956522

Combine like terms: 0.094425601 + 0.1086956522 = 0.2031212532
x = 0.2031212532

Simplifying
x = 0.2031212532

Subproblem 2
x + -0.1086956522 = -0.094425601

Simplifying
x + -0.1086956522 = -0.094425601

Reorder the terms:
-0.1086956522 + x = -0.094425601

Solving
-0.1086956522 + x = -0.094425601

Solving for variable 'x'.

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

Add '0.1086956522' to each side of the equation.
-0.1086956522 + 0.1086956522 + x = -0.094425601 + 0.1086956522

Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000
0.0000000000 + x = -0.094425601 + 0.1086956522
x = -0.094425601 + 0.1086956522

Combine like terms: -0.094425601 + 0.1086956522 = 0.0142700512
x = 0.0142700512

Simplifying
x = 0.0142700512

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2031212532, 0.0142700512}
Solution
x = {0.2031212532, 0.0142700512}