(14x-22)(x+11)=240

Solution for (14x-22)(x+11)=240 equation:

Simplifying
(14x + -22)(x + 11) = 240

Reorder the terms:
(-22 + 14x)(x + 11) = 240

Reorder the terms:
(-22 + 14x)(11 + x) = 240

Multiply (-22 + 14x) * (11 + x)
(-22(11 + x) + 14x * (11 + x)) = 240
((11 * -22 + x * -22) + 14x * (11 + x)) = 240
((-242 + -22x) + 14x * (11 + x)) = 240
(-242 + -22x + (11 * 14x + x * 14x)) = 240
(-242 + -22x + (154x + 14x2)) = 240

Combine like terms: -22x + 154x = 132x
(-242 + 132x + 14x2) = 240

Solving
-242 + 132x + 14x2 = 240

Solving for variable 'x'.

Reorder the terms:
-242 + -240 + 132x + 14x2 = 240 + -240

Combine like terms: -242 + -240 = -482
-482 + 132x + 14x2 = 240 + -240

Combine like terms: 240 + -240 = 0
-482 + 132x + 14x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-241 + 66x + 7x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-241 + 66x + 7x2)' equal to zero and attempt to solve:

Simplifying
-241 + 66x + 7x2 = 0

Solving
-241 + 66x + 7x2 = 0

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

Divide each side by '7'.
-34.42857143 + 9.428571429x + x2 = 0

Move the constant term to the right:

Add '34.42857143' to each side of the equation.
-34.42857143 + 9.428571429x + 34.42857143 + x2 = 0 + 34.42857143

Reorder the terms:
-34.42857143 + 34.42857143 + 9.428571429x + x2 = 0 + 34.42857143

Combine like terms: -34.42857143 + 34.42857143 = 0.00000000
0.00000000 + 9.428571429x + x2 = 0 + 34.42857143
9.428571429x + x2 = 0 + 34.42857143

Combine like terms: 0 + 34.42857143 = 34.42857143
9.428571429x + x2 = 34.42857143

The x term is 9.428571429x.  Take half its coefficient (4.714285715).
Square it (22.22448980) and add it to both sides.

Add '22.22448980' to each side of the equation.
9.428571429x + 22.22448980 + x2 = 34.42857143 + 22.22448980

Reorder the terms:
22.22448980 + 9.428571429x + x2 = 34.42857143 + 22.22448980

Combine like terms: 34.42857143 + 22.22448980 = 56.65306123
22.22448980 + 9.428571429x + x2 = 56.65306123

Factor a perfect square on the left side:
(x + 4.714285715)(x + 4.714285715) = 56.65306123

Calculate the square root of the right side: 7.526822785

Break this problem into two subproblems by setting 
(x + 4.714285715) equal to 7.526822785 and -7.526822785.

Subproblem 1
x + 4.714285715 = 7.526822785

Simplifying
x + 4.714285715 = 7.526822785

Reorder the terms:
4.714285715 + x = 7.526822785

Solving
4.714285715 + x = 7.526822785

Solving for variable 'x'.

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

Add '-4.714285715' to each side of the equation.
4.714285715 + -4.714285715 + x = 7.526822785 + -4.714285715

Combine like terms: 4.714285715 + -4.714285715 = 0.000000000
0.000000000 + x = 7.526822785 + -4.714285715
x = 7.526822785 + -4.714285715

Combine like terms: 7.526822785 + -4.714285715 = 2.81253707
x = 2.81253707

Simplifying
x = 2.81253707

Subproblem 2
x + 4.714285715 = -7.526822785

Simplifying
x + 4.714285715 = -7.526822785

Reorder the terms:
4.714285715 + x = -7.526822785

Solving
4.714285715 + x = -7.526822785

Solving for variable 'x'.

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

Add '-4.714285715' to each side of the equation.
4.714285715 + -4.714285715 + x = -7.526822785 + -4.714285715

Combine like terms: 4.714285715 + -4.714285715 = 0.000000000
0.000000000 + x = -7.526822785 + -4.714285715
x = -7.526822785 + -4.714285715

Combine like terms: -7.526822785 + -4.714285715 = -12.2411085
x = -12.2411085

Simplifying
x = -12.2411085

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.81253707, -12.2411085}
Solution
x = {2.81253707, -12.2411085}