(19-4x)(2x+23)=57

Solution for (19-4x)(2x+23)=57 equation:

Simplifying
(19 + -4x)(2x + 23) = 57

Reorder the terms:
(19 + -4x)(23 + 2x) = 57

Multiply (19 + -4x) * (23 + 2x)
(19(23 + 2x) + -4x * (23 + 2x)) = 57
((23 * 19 + 2x * 19) + -4x * (23 + 2x)) = 57
((437 + 38x) + -4x * (23 + 2x)) = 57
(437 + 38x + (23 * -4x + 2x * -4x)) = 57
(437 + 38x + (-92x + -8x2)) = 57

Combine like terms: 38x + -92x = -54x
(437 + -54x + -8x2) = 57

Solving
437 + -54x + -8x2 = 57

Solving for variable 'x'.

Reorder the terms:
437 + -57 + -54x + -8x2 = 57 + -57

Combine like terms: 437 + -57 = 380
380 + -54x + -8x2 = 57 + -57

Combine like terms: 57 + -57 = 0
380 + -54x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(190 + -27x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(190 + -27x + -4x2)' equal to zero and attempt to solve:

Simplifying
190 + -27x + -4x2 = 0

Solving
190 + -27x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-47.5 + 6.75x + x2 = 0

Move the constant term to the right:

Add '47.5' to each side of the equation.
-47.5 + 6.75x + 47.5 + x2 = 0 + 47.5

Reorder the terms:
-47.5 + 47.5 + 6.75x + x2 = 0 + 47.5

Combine like terms: -47.5 + 47.5 = 0.0
0.0 + 6.75x + x2 = 0 + 47.5
6.75x + x2 = 0 + 47.5

Combine like terms: 0 + 47.5 = 47.5
6.75x + x2 = 47.5

The x term is 6.75x.  Take half its coefficient (3.375).
Square it (11.390625) and add it to both sides.

Add '11.390625' to each side of the equation.
6.75x + 11.390625 + x2 = 47.5 + 11.390625

Reorder the terms:
11.390625 + 6.75x + x2 = 47.5 + 11.390625

Combine like terms: 47.5 + 11.390625 = 58.890625
11.390625 + 6.75x + x2 = 58.890625

Factor a perfect square on the left side:
(x + 3.375)(x + 3.375) = 58.890625

Calculate the square root of the right side: 7.674022739

Break this problem into two subproblems by setting 
(x + 3.375) equal to 7.674022739 and -7.674022739.

Subproblem 1
x + 3.375 = 7.674022739

Simplifying
x + 3.375 = 7.674022739

Reorder the terms:
3.375 + x = 7.674022739

Solving
3.375 + x = 7.674022739

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = 7.674022739 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = 7.674022739 + -3.375
x = 7.674022739 + -3.375

Combine like terms: 7.674022739 + -3.375 = 4.299022739
x = 4.299022739

Simplifying
x = 4.299022739

Subproblem 2
x + 3.375 = -7.674022739

Simplifying
x + 3.375 = -7.674022739

Reorder the terms:
3.375 + x = -7.674022739

Solving
3.375 + x = -7.674022739

Solving for variable 'x'.

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

Add '-3.375' to each side of the equation.
3.375 + -3.375 + x = -7.674022739 + -3.375

Combine like terms: 3.375 + -3.375 = 0.000
0.000 + x = -7.674022739 + -3.375
x = -7.674022739 + -3.375

Combine like terms: -7.674022739 + -3.375 = -11.049022739
x = -11.049022739

Simplifying
x = -11.049022739

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.299022739, -11.049022739}
Solution
x = {4.299022739, -11.049022739}