4(x-5)11(x-1)=5-7(x-2)

Solution for 4(x-5)11(x-1)=5-7(x-2) equation:

Simplifying
4(x + -5) * 11(x + -1) = 5 + -7(x + -2)

Reorder the terms:
4(-5 + x) * 11(x + -1) = 5 + -7(x + -2)

Reorder the terms:
4(-5 + x) * 11(-1 + x) = 5 + -7(x + -2)

Reorder the terms for easier multiplication:
4 * 11(-5 + x)(-1 + x) = 5 + -7(x + -2)

Multiply 4 * 11
44(-5 + x)(-1 + x) = 5 + -7(x + -2)

Multiply (-5 + x) * (-1 + x)
44(-5(-1 + x) + x(-1 + x)) = 5 + -7(x + -2)
44((-1 * -5 + x * -5) + x(-1 + x)) = 5 + -7(x + -2)
44((5 + -5x) + x(-1 + x)) = 5 + -7(x + -2)
44(5 + -5x + (-1 * x + x * x)) = 5 + -7(x + -2)
44(5 + -5x + (-1x + x2)) = 5 + -7(x + -2)

Combine like terms: -5x + -1x = -6x
44(5 + -6x + x2) = 5 + -7(x + -2)
(5 * 44 + -6x * 44 + x2 * 44) = 5 + -7(x + -2)
(220 + -264x + 44x2) = 5 + -7(x + -2)

Reorder the terms:
220 + -264x + 44x2 = 5 + -7(-2 + x)
220 + -264x + 44x2 = 5 + (-2 * -7 + x * -7)
220 + -264x + 44x2 = 5 + (14 + -7x)

Combine like terms: 5 + 14 = 19
220 + -264x + 44x2 = 19 + -7x

Solving
220 + -264x + 44x2 = 19 + -7x

Solving for variable 'x'.

Reorder the terms:
220 + -19 + -264x + 7x + 44x2 = 19 + -7x + -19 + 7x

Combine like terms: 220 + -19 = 201
201 + -264x + 7x + 44x2 = 19 + -7x + -19 + 7x

Combine like terms: -264x + 7x = -257x
201 + -257x + 44x2 = 19 + -7x + -19 + 7x

Reorder the terms:
201 + -257x + 44x2 = 19 + -19 + -7x + 7x

Combine like terms: 19 + -19 = 0
201 + -257x + 44x2 = 0 + -7x + 7x
201 + -257x + 44x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
201 + -257x + 44x2 = 0

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

Divide each side by '44'.
4.568181818 + -5.840909091x + x2 = 0

Move the constant term to the right:

Add '-4.568181818' to each side of the equation.
4.568181818 + -5.840909091x + -4.568181818 + x2 = 0 + -4.568181818

Reorder the terms:
4.568181818 + -4.568181818 + -5.840909091x + x2 = 0 + -4.568181818

Combine like terms: 4.568181818 + -4.568181818 = 0.000000000
0.000000000 + -5.840909091x + x2 = 0 + -4.568181818
-5.840909091x + x2 = 0 + -4.568181818

Combine like terms: 0 + -4.568181818 = -4.568181818
-5.840909091x + x2 = -4.568181818

The x term is -5.840909091x.  Take half its coefficient (-2.920454546).
Square it (8.529054755) and add it to both sides.

Add '8.529054755' to each side of the equation.
-5.840909091x + 8.529054755 + x2 = -4.568181818 + 8.529054755

Reorder the terms:
8.529054755 + -5.840909091x + x2 = -4.568181818 + 8.529054755

Combine like terms: -4.568181818 + 8.529054755 = 3.960872937
8.529054755 + -5.840909091x + x2 = 3.960872937

Factor a perfect square on the left side:
(x + -2.920454546)(x + -2.920454546) = 3.960872937

Calculate the square root of the right side: 1.990194196

Break this problem into two subproblems by setting 
(x + -2.920454546) equal to 1.990194196 and -1.990194196.

Subproblem 1
x + -2.920454546 = 1.990194196

Simplifying
x + -2.920454546 = 1.990194196

Reorder the terms:
-2.920454546 + x = 1.990194196

Solving
-2.920454546 + x = 1.990194196

Solving for variable 'x'.

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

Add '2.920454546' to each side of the equation.
-2.920454546 + 2.920454546 + x = 1.990194196 + 2.920454546

Combine like terms: -2.920454546 + 2.920454546 = 0.000000000
0.000000000 + x = 1.990194196 + 2.920454546
x = 1.990194196 + 2.920454546

Combine like terms: 1.990194196 + 2.920454546 = 4.910648742
x = 4.910648742

Simplifying
x = 4.910648742

Subproblem 2
x + -2.920454546 = -1.990194196

Simplifying
x + -2.920454546 = -1.990194196

Reorder the terms:
-2.920454546 + x = -1.990194196

Solving
-2.920454546 + x = -1.990194196

Solving for variable 'x'.

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

Add '2.920454546' to each side of the equation.
-2.920454546 + 2.920454546 + x = -1.990194196 + 2.920454546

Combine like terms: -2.920454546 + 2.920454546 = 0.000000000
0.000000000 + x = -1.990194196 + 2.920454546
x = -1.990194196 + 2.920454546

Combine like terms: -1.990194196 + 2.920454546 = 0.93026035
x = 0.93026035

Simplifying
x = 0.93026035

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.910648742, 0.93026035}