(3x-4)(x+8)=(x+22)(1-2x)

Solution for (3x-4)(x+8)=(x+22)(1-2x) equation:

Simplifying
(3x + -4)(x + 8) = (x + 22)(1 + -2x)

Reorder the terms:
(-4 + 3x)(x + 8) = (x + 22)(1 + -2x)

Reorder the terms:
(-4 + 3x)(8 + x) = (x + 22)(1 + -2x)

Multiply (-4 + 3x) * (8 + x)
(-4(8 + x) + 3x * (8 + x)) = (x + 22)(1 + -2x)
((8 * -4 + x * -4) + 3x * (8 + x)) = (x + 22)(1 + -2x)
((-32 + -4x) + 3x * (8 + x)) = (x + 22)(1 + -2x)
(-32 + -4x + (8 * 3x + x * 3x)) = (x + 22)(1 + -2x)
(-32 + -4x + (24x + 3x2)) = (x + 22)(1 + -2x)

Combine like terms: -4x + 24x = 20x
(-32 + 20x + 3x2) = (x + 22)(1 + -2x)

Reorder the terms:
-32 + 20x + 3x2 = (22 + x)(1 + -2x)

Multiply (22 + x) * (1 + -2x)
-32 + 20x + 3x2 = (22(1 + -2x) + x(1 + -2x))
-32 + 20x + 3x2 = ((1 * 22 + -2x * 22) + x(1 + -2x))
-32 + 20x + 3x2 = ((22 + -44x) + x(1 + -2x))
-32 + 20x + 3x2 = (22 + -44x + (1 * x + -2x * x))
-32 + 20x + 3x2 = (22 + -44x + (1x + -2x2))

Combine like terms: -44x + 1x = -43x
-32 + 20x + 3x2 = (22 + -43x + -2x2)

Solving
-32 + 20x + 3x2 = 22 + -43x + -2x2

Solving for variable 'x'.

Reorder the terms:
-32 + -22 + 20x + 43x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: -32 + -22 = -54
-54 + 20x + 43x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: 20x + 43x = 63x
-54 + 63x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
-54 + 63x + 5x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Reorder the terms:
-54 + 63x + 5x2 = 22 + -22 + -43x + 43x + -2x2 + 2x2

Combine like terms: 22 + -22 = 0
-54 + 63x + 5x2 = 0 + -43x + 43x + -2x2 + 2x2
-54 + 63x + 5x2 = -43x + 43x + -2x2 + 2x2

Combine like terms: -43x + 43x = 0
-54 + 63x + 5x2 = 0 + -2x2 + 2x2
-54 + 63x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-54 + 63x + 5x2 = 0

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

Divide each side by '5'.
-10.8 + 12.6x + x2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + 12.6x + 10.8 + x2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + 12.6x + x2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + 12.6x + x2 = 0 + 10.8
12.6x + x2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
12.6x + x2 = 10.8

The x term is 12.6x.  Take half its coefficient (6.3).
Square it (39.69) and add it to both sides.

Add '39.69' to each side of the equation.
12.6x + 39.69 + x2 = 10.8 + 39.69

Reorder the terms:
39.69 + 12.6x + x2 = 10.8 + 39.69

Combine like terms: 10.8 + 39.69 = 50.49
39.69 + 12.6x + x2 = 50.49

Factor a perfect square on the left side:
(x + 6.3)(x + 6.3) = 50.49

Calculate the square root of the right side: 7.105631569

Break this problem into two subproblems by setting 
(x + 6.3) equal to 7.105631569 and -7.105631569.

Subproblem 1
x + 6.3 = 7.105631569

Simplifying
x + 6.3 = 7.105631569

Reorder the terms:
6.3 + x = 7.105631569

Solving
6.3 + x = 7.105631569

Solving for variable 'x'.

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

Add '-6.3' to each side of the equation.
6.3 + -6.3 + x = 7.105631569 + -6.3

Combine like terms: 6.3 + -6.3 = 0.0
0.0 + x = 7.105631569 + -6.3
x = 7.105631569 + -6.3

Combine like terms: 7.105631569 + -6.3 = 0.805631569
x = 0.805631569

Simplifying
x = 0.805631569

Subproblem 2
x + 6.3 = -7.105631569

Simplifying
x + 6.3 = -7.105631569

Reorder the terms:
6.3 + x = -7.105631569

Solving
6.3 + x = -7.105631569

Solving for variable 'x'.

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

Add '-6.3' to each side of the equation.
6.3 + -6.3 + x = -7.105631569 + -6.3

Combine like terms: 6.3 + -6.3 = 0.0
0.0 + x = -7.105631569 + -6.3
x = -7.105631569 + -6.3

Combine like terms: -7.105631569 + -6.3 = -13.405631569
x = -13.405631569

Simplifying
x = -13.405631569

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.805631569, -13.405631569}