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

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

Simplifying
x + sqrt((X + 6)(x + -2)) = 2 + sqrt(x + 6) + sqrt(x + -2)

Reorder the terms:
x + qrst((6 + X)(x + -2)) = 2 + sqrt(x + 6) + sqrt(x + -2)

Reorder the terms:
x + qrst((6 + X)(-2 + x)) = 2 + sqrt(x + 6) + sqrt(x + -2)

Multiply (6 + X) * (-2 + x)
x + qrst((6(-2 + x) + X(-2 + x))) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + qrst(((-2 * 6 + x * 6) + X(-2 + x))) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + qrst(((-12 + 6x) + X(-2 + x))) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + qrst((-12 + 6x + (-2 * X + x * X))) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + qrst((-12 + 6x + (-2X + xX))) = 2 + sqrt(x + 6) + sqrt(x + -2)

Reorder the terms:
x + qrst((-12 + -2X + 6x + xX)) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + qrst((-12 + -2X + 6x + xX)) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + (-12 * qrst + -2X * qrst + 6x * qrst + xX * qrst) = 2 + sqrt(x + 6) + sqrt(x + -2)
x + (-12qrst + -2qrstX + 6qrstx + qrstxX) = 2 + sqrt(x + 6) + sqrt(x + -2)

Reorder the terms:
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + sqrt(x + 6) + sqrt(x + -2)

Reorder the terms:
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + qrst(6 + x) + sqrt(x + -2)
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + (6 * qrst + x * qrst) + sqrt(x + -2)
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + (6qrst + qrstx) + sqrt(x + -2)

Reorder the terms:
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 6qrst + qrstx + qrst(-2 + x)
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 6qrst + qrstx + (-2 * qrst + x * qrst)
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 6qrst + qrstx + (-2qrst + qrstx)

Reorder the terms:
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 6qrst + -2qrst + qrstx + qrstx

Combine like terms: 6qrst + -2qrst = 4qrst
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 4qrst + qrstx + qrstx

Combine like terms: qrstx + qrstx = 2qrstx
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 4qrst + 2qrstx

Solving
-12qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 4qrst + 2qrstx

Solving for variable 'q'.

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

Add '-4qrst' to each side of the equation.
-12qrst + -2qrstX + 6qrstx + qrstxX + -4qrst + x = 2 + 4qrst + -4qrst + 2qrstx

Reorder the terms:
-12qrst + -4qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 4qrst + -4qrst + 2qrstx

Combine like terms: -12qrst + -4qrst = -16qrst
-16qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 4qrst + -4qrst + 2qrstx

Combine like terms: 4qrst + -4qrst = 0
-16qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 0 + 2qrstx
-16qrst + -2qrstX + 6qrstx + qrstxX + x = 2 + 2qrstx

Add '-2qrstx' to each side of the equation.
-16qrst + -2qrstX + 6qrstx + qrstxX + -2qrstx + x = 2 + 2qrstx + -2qrstx

Reorder the terms:
-16qrst + -2qrstX + 6qrstx + -2qrstx + qrstxX + x = 2 + 2qrstx + -2qrstx

Combine like terms: 6qrstx + -2qrstx = 4qrstx
-16qrst + -2qrstX + 4qrstx + qrstxX + x = 2 + 2qrstx + -2qrstx

Combine like terms: 2qrstx + -2qrstx = 0
-16qrst + -2qrstX + 4qrstx + qrstxX + x = 2 + 0
-16qrst + -2qrstX + 4qrstx + qrstxX + x = 2

Add '-1x' to each side of the equation.
-16qrst + -2qrstX + 4qrstx + qrstxX + x + -1x = 2 + -1x

Combine like terms: x + -1x = 0
-16qrst + -2qrstX + 4qrstx + qrstxX + 0 = 2 + -1x
-16qrst + -2qrstX + 4qrstx + qrstxX = 2 + -1x

Reorder the terms:
-2 + -16qrst + -2qrstX + 4qrstx + qrstxX + x = 2 + -1x + -2 + x

Reorder the terms:
-2 + -16qrst + -2qrstX + 4qrstx + qrstxX + x = 2 + -2 + -1x + x

Combine like terms: 2 + -2 = 0
-2 + -16qrst + -2qrstX + 4qrstx + qrstxX + x = 0 + -1x + x
-2 + -16qrst + -2qrstX + 4qrstx + qrstxX + x = -1x + x

Combine like terms: -1x + x = 0
-2 + -16qrst + -2qrstX + 4qrstx + qrstxX + x = 0

The solution to this equation could not be determined.