-2(x-11)19x=54

Solution for -2(x-11)19x=54 equation:

Simplifying
-2(x + -11) * 19x = 54

Reorder the terms:
-2(-11 + x) * 19x = 54

Reorder the terms for easier multiplication:
-2 * 19x(-11 + x) = 54

Multiply -2 * 19
-38x(-11 + x) = 54
(-11 * -38x + x * -38x) = 54
(418x + -38x2) = 54

Solving
418x + -38x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + 418x + -38x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + 418x + -38x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 209x + -19x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-27 + 209x + -19x2)' equal to zero and attempt to solve:

Simplifying
-27 + 209x + -19x2 = 0

Solving
-27 + 209x + -19x2 = 0

Begin completing the square.  Divide all terms by
-19 the coefficient of the squared term: 

Divide each side by '-19'.
1.421052632 + -11x + x2 = 0

Move the constant term to the right:

Add '-1.421052632' to each side of the equation.
1.421052632 + -11x + -1.421052632 + x2 = 0 + -1.421052632

Reorder the terms:
1.421052632 + -1.421052632 + -11x + x2 = 0 + -1.421052632

Combine like terms: 1.421052632 + -1.421052632 = 0.000000000
0.000000000 + -11x + x2 = 0 + -1.421052632
-11x + x2 = 0 + -1.421052632

Combine like terms: 0 + -1.421052632 = -1.421052632
-11x + x2 = -1.421052632

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = -1.421052632 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -1.421052632 + 30.25

Combine like terms: -1.421052632 + 30.25 = 28.828947368
30.25 + -11x + x2 = 28.828947368

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 28.828947368

Calculate the square root of the right side: 5.36925948

Break this problem into two subproblems by setting 
(x + -5.5) equal to 5.36925948 and -5.36925948.

Subproblem 1
x + -5.5 = 5.36925948

Simplifying
x + -5.5 = 5.36925948

Reorder the terms:
-5.5 + x = 5.36925948

Solving
-5.5 + x = 5.36925948

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 5.36925948 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 5.36925948 + 5.5
x = 5.36925948 + 5.5

Combine like terms: 5.36925948 + 5.5 = 10.86925948
x = 10.86925948

Simplifying
x = 10.86925948

Subproblem 2
x + -5.5 = -5.36925948

Simplifying
x + -5.5 = -5.36925948

Reorder the terms:
-5.5 + x = -5.36925948

Solving
-5.5 + x = -5.36925948

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -5.36925948 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -5.36925948 + 5.5
x = -5.36925948 + 5.5

Combine like terms: -5.36925948 + 5.5 = 0.13074052
x = 0.13074052

Simplifying
x = 0.13074052

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.86925948, 0.13074052}
Solution
x = {10.86925948, 0.13074052}