(X+2)x(X+6)=(X+4)x(2x-2)

Solution for (X+2)x(X+6)=(X+4)x(2x-2) equation:

Simplifying
(X + 2) * x(X + 6) = (X + 4) * x(2x + -2)

Reorder the terms:
(2 + X) * x(X + 6) = (X + 4) * x(2x + -2)

Reorder the terms:
(2 + X) * x(6 + X) = (X + 4) * x(2x + -2)

Reorder the terms for easier multiplication:
x(2 + X)(6 + X) = (X + 4) * x(2x + -2)

Multiply (2 + X) * (6 + X)
x(2(6 + X) + X(6 + X)) = (X + 4) * x(2x + -2)
x((6 * 2 + X * 2) + X(6 + X)) = (X + 4) * x(2x + -2)
x((12 + 2X) + X(6 + X)) = (X + 4) * x(2x + -2)
x(12 + 2X + (6 * X + X * X)) = (X + 4) * x(2x + -2)
x(12 + 2X + (6X + X2)) = (X + 4) * x(2x + -2)

Combine like terms: 2X + 6X = 8X
x(12 + 8X + X2) = (X + 4) * x(2x + -2)
(12 * x + 8X * x + X2 * x) = (X + 4) * x(2x + -2)
(12x + 8xX + xX2) = (X + 4) * x(2x + -2)

Reorder the terms:
12x + 8xX + xX2 = (4 + X) * x(2x + -2)

Reorder the terms:
12x + 8xX + xX2 = (4 + X) * x(-2 + 2x)

Reorder the terms for easier multiplication:
12x + 8xX + xX2 = x(4 + X)(-2 + 2x)

Multiply (4 + X) * (-2 + 2x)
12x + 8xX + xX2 = x(4(-2 + 2x) + X(-2 + 2x))
12x + 8xX + xX2 = x((-2 * 4 + 2x * 4) + X(-2 + 2x))
12x + 8xX + xX2 = x((-8 + 8x) + X(-2 + 2x))
12x + 8xX + xX2 = x(-8 + 8x + (-2 * X + 2x * X))
12x + 8xX + xX2 = x(-8 + 8x + (-2X + 2xX))

Reorder the terms:
12x + 8xX + xX2 = x(-8 + -2X + 8x + 2xX)
12x + 8xX + xX2 = x(-8 + -2X + 8x + 2xX)
12x + 8xX + xX2 = (-8 * x + -2X * x + 8x * x + 2xX * x)
12x + 8xX + xX2 = (-8x + -2xX + 8x2 + 2x2X)

Solving
12x + 8xX + xX2 = -8x + -2xX + 8x2 + 2x2X

Solving for variable 'x'.

Reorder the terms:
12x + 8x + 8xX + 2xX + xX2 + -8x2 + -2x2X = -8x + -2xX + 8x2 + 2x2X + 8x + 2xX + -8x2 + -2x2X

Combine like terms: 12x + 8x = 20x
20x + 8xX + 2xX + xX2 + -8x2 + -2x2X = -8x + -2xX + 8x2 + 2x2X + 8x + 2xX + -8x2 + -2x2X

Combine like terms: 8xX + 2xX = 10xX
20x + 10xX + xX2 + -8x2 + -2x2X = -8x + -2xX + 8x2 + 2x2X + 8x + 2xX + -8x2 + -2x2X

Reorder the terms:
20x + 10xX + xX2 + -8x2 + -2x2X = -8x + 8x + -2xX + 2xX + 8x2 + -8x2 + 2x2X + -2x2X

Combine like terms: -8x + 8x = 0
20x + 10xX + xX2 + -8x2 + -2x2X = 0 + -2xX + 2xX + 8x2 + -8x2 + 2x2X + -2x2X
20x + 10xX + xX2 + -8x2 + -2x2X = -2xX + 2xX + 8x2 + -8x2 + 2x2X + -2x2X

Combine like terms: -2xX + 2xX = 0
20x + 10xX + xX2 + -8x2 + -2x2X = 0 + 8x2 + -8x2 + 2x2X + -2x2X
20x + 10xX + xX2 + -8x2 + -2x2X = 8x2 + -8x2 + 2x2X + -2x2X

Combine like terms: 8x2 + -8x2 = 0
20x + 10xX + xX2 + -8x2 + -2x2X = 0 + 2x2X + -2x2X
20x + 10xX + xX2 + -8x2 + -2x2X = 2x2X + -2x2X

Combine like terms: 2x2X + -2x2X = 0
20x + 10xX + xX2 + -8x2 + -2x2X = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + 10X + X2 + -8x + -2xX) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(20 + 10X + X2 + -8x + -2xX)' equal to zero and attempt to solve:

Simplifying
20 + 10X + X2 + -8x + -2xX = 0

Solving
20 + 10X + X2 + -8x + -2xX = 0

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

Add '-20' to each side of the equation.
20 + 10X + X2 + -8x + -20 + -2xX = 0 + -20

Reorder the terms:
20 + -20 + 10X + X2 + -8x + -2xX = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 10X + X2 + -8x + -2xX = 0 + -20
10X + X2 + -8x + -2xX = 0 + -20

Combine like terms: 0 + -20 = -20
10X + X2 + -8x + -2xX = -20

Add '-10X' to each side of the equation.
10X + X2 + -8x + -10X + -2xX = -20 + -10X

Reorder the terms:
10X + -10X + X2 + -8x + -2xX = -20 + -10X

Combine like terms: 10X + -10X = 0
0 + X2 + -8x + -2xX = -20 + -10X
X2 + -8x + -2xX = -20 + -10X

Add '-1X2' to each side of the equation.
X2 + -8x + -1X2 + -2xX = -20 + -10X + -1X2

Reorder the terms:
X2 + -1X2 + -8x + -2xX = -20 + -10X + -1X2

Combine like terms: X2 + -1X2 = 0
0 + -8x + -2xX = -20 + -10X + -1X2
-8x + -2xX = -20 + -10X + -1X2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}