19x(6x-3)23=123

Solution for 19x(6x-3)23=123 equation:

Simplifying
19x(6x + -3) * 23 = 123

Reorder the terms:
19x(-3 + 6x) * 23 = 123

Reorder the terms for easier multiplication:
19 * 23x(-3 + 6x) = 123

Multiply 19 * 23
437x(-3 + 6x) = 123
(-3 * 437x + 6x * 437x) = 123
(-1311x + 2622x2) = 123

Solving
-1311x + 2622x2 = 123

Solving for variable 'x'.

Reorder the terms:
-123 + -1311x + 2622x2 = 123 + -123

Combine like terms: 123 + -123 = 0
-123 + -1311x + 2622x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-41 + -437x + 874x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-41 + -437x + 874x2)' equal to zero and attempt to solve:

Simplifying
-41 + -437x + 874x2 = 0

Solving
-41 + -437x + 874x2 = 0

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

Divide each side by '874'.
-0.04691075515 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.04691075515' to each side of the equation.
-0.04691075515 + -0.5x + 0.04691075515 + x2 = 0 + 0.04691075515

Reorder the terms:
-0.04691075515 + 0.04691075515 + -0.5x + x2 = 0 + 0.04691075515

Combine like terms: -0.04691075515 + 0.04691075515 = 0.00000000000
0.00000000000 + -0.5x + x2 = 0 + 0.04691075515
-0.5x + x2 = 0 + 0.04691075515

Combine like terms: 0 + 0.04691075515 = 0.04691075515
-0.5x + x2 = 0.04691075515

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.04691075515 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.04691075515 + 0.0625

Combine like terms: 0.04691075515 + 0.0625 = 0.10941075515
0.0625 + -0.5x + x2 = 0.10941075515

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.10941075515

Calculate the square root of the right side: 0.330772966

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.330772966 and -0.330772966.

Subproblem 1
x + -0.25 = 0.330772966

Simplifying
x + -0.25 = 0.330772966

Reorder the terms:
-0.25 + x = 0.330772966

Solving
-0.25 + x = 0.330772966

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.330772966 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.330772966 + 0.25
x = 0.330772966 + 0.25

Combine like terms: 0.330772966 + 0.25 = 0.580772966
x = 0.580772966

Simplifying
x = 0.580772966

Subproblem 2
x + -0.25 = -0.330772966

Simplifying
x + -0.25 = -0.330772966

Reorder the terms:
-0.25 + x = -0.330772966

Solving
-0.25 + x = -0.330772966

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.330772966 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.330772966 + 0.25
x = -0.330772966 + 0.25

Combine like terms: -0.330772966 + 0.25 = -0.080772966
x = -0.080772966

Simplifying
x = -0.080772966

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.580772966, -0.080772966}
Solution
x = {0.580772966, -0.080772966}