11(12+14x)15(14-5x)=263

Solution for 11(12+14x)15(14-5x)=263 equation:

Simplifying
11(12 + 14x) * 15(14 + -5x) = 263

Reorder the terms for easier multiplication:
11 * 15(12 + 14x)(14 + -5x) = 263

Multiply 11 * 15
165(12 + 14x)(14 + -5x) = 263

Multiply (12 + 14x) * (14 + -5x)
165(12(14 + -5x) + 14x * (14 + -5x)) = 263
165((14 * 12 + -5x * 12) + 14x * (14 + -5x)) = 263
165((168 + -60x) + 14x * (14 + -5x)) = 263
165(168 + -60x + (14 * 14x + -5x * 14x)) = 263
165(168 + -60x + (196x + -70x2)) = 263

Combine like terms: -60x + 196x = 136x
165(168 + 136x + -70x2) = 263
(168 * 165 + 136x * 165 + -70x2 * 165) = 263
(27720 + 22440x + -11550x2) = 263

Solving
27720 + 22440x + -11550x2 = 263

Solving for variable 'x'.

Reorder the terms:
27720 + -263 + 22440x + -11550x2 = 263 + -263

Combine like terms: 27720 + -263 = 27457
27457 + 22440x + -11550x2 = 263 + -263

Combine like terms: 263 + -263 = 0
27457 + 22440x + -11550x2 = 0

Begin completing the square.  Divide all terms by
-11550 the coefficient of the squared term: 

Divide each side by '-11550'.
-2.377229437 + -1.942857143x + x2 = 0.0

Move the constant term to the right:

Add '2.377229437' to each side of the equation.
-2.377229437 + -1.942857143x + 2.377229437 + x2 = 0.0 + 2.377229437

Reorder the terms:
-2.377229437 + 2.377229437 + -1.942857143x + x2 = 0.0 + 2.377229437

Combine like terms: -2.377229437 + 2.377229437 = 0.000000000
0.000000000 + -1.942857143x + x2 = 0.0 + 2.377229437
-1.942857143x + x2 = 0.0 + 2.377229437

Combine like terms: 0.0 + 2.377229437 = 2.377229437
-1.942857143x + x2 = 2.377229437

The x term is -1.942857143x.  Take half its coefficient (-0.9714285715).
Square it (0.9436734695) and add it to both sides.

Add '0.9436734695' to each side of the equation.
-1.942857143x + 0.9436734695 + x2 = 2.377229437 + 0.9436734695

Reorder the terms:
0.9436734695 + -1.942857143x + x2 = 2.377229437 + 0.9436734695

Combine like terms: 2.377229437 + 0.9436734695 = 3.3209029065
0.9436734695 + -1.942857143x + x2 = 3.3209029065

Factor a perfect square on the left side:
(x + -0.9714285715)(x + -0.9714285715) = 3.3209029065

Calculate the square root of the right side: 1.822334466

Break this problem into two subproblems by setting 
(x + -0.9714285715) equal to 1.822334466 and -1.822334466.

Subproblem 1
x + -0.9714285715 = 1.822334466

Simplifying
x + -0.9714285715 = 1.822334466

Reorder the terms:
-0.9714285715 + x = 1.822334466

Solving
-0.9714285715 + x = 1.822334466

Solving for variable 'x'.

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

Add '0.9714285715' to each side of the equation.
-0.9714285715 + 0.9714285715 + x = 1.822334466 + 0.9714285715

Combine like terms: -0.9714285715 + 0.9714285715 = 0.0000000000
0.0000000000 + x = 1.822334466 + 0.9714285715
x = 1.822334466 + 0.9714285715

Combine like terms: 1.822334466 + 0.9714285715 = 2.7937630375
x = 2.7937630375

Simplifying
x = 2.7937630375

Subproblem 2
x + -0.9714285715 = -1.822334466

Simplifying
x + -0.9714285715 = -1.822334466

Reorder the terms:
-0.9714285715 + x = -1.822334466

Solving
-0.9714285715 + x = -1.822334466

Solving for variable 'x'.

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

Add '0.9714285715' to each side of the equation.
-0.9714285715 + 0.9714285715 + x = -1.822334466 + 0.9714285715

Combine like terms: -0.9714285715 + 0.9714285715 = 0.0000000000
0.0000000000 + x = -1.822334466 + 0.9714285715
x = -1.822334466 + 0.9714285715

Combine like terms: -1.822334466 + 0.9714285715 = -0.8509058945
x = -0.8509058945

Simplifying
x = -0.8509058945

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.7937630375, -0.8509058945}