(x-y)(x+y)=2(y+6)

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

Simplifying
(x + -1y)(x + y) = 2(y + 6)

Multiply (x + -1y) * (x + y)
(x(x + y) + -1y * (x + y)) = 2(y + 6)
((x * x + y * x) + -1y * (x + y)) = 2(y + 6)

Reorder the terms:
((xy + x2) + -1y * (x + y)) = 2(y + 6)
((xy + x2) + -1y * (x + y)) = 2(y + 6)
(xy + x2 + (x * -1y + y * -1y)) = 2(y + 6)
(xy + x2 + (-1xy + -1y2)) = 2(y + 6)

Reorder the terms:
(xy + -1xy + x2 + -1y2) = 2(y + 6)

Combine like terms: xy + -1xy = 0
(0 + x2 + -1y2) = 2(y + 6)
(x2 + -1y2) = 2(y + 6)

Reorder the terms:
x2 + -1y2 = 2(6 + y)
x2 + -1y2 = (6 * 2 + y * 2)
x2 + -1y2 = (12 + 2y)

Solving
x2 + -1y2 = 12 + 2y

Solving for variable 'x'.

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

Add 'y2' to each side of the equation.
x2 + -1y2 + y2 = 12 + 2y + y2

Combine like terms: -1y2 + y2 = 0
x2 + 0 = 12 + 2y + y2
x2 = 12 + 2y + y2

Simplifying
x2 = 12 + 2y + y2

Reorder the terms:
-12 + x2 + -2y + -1y2 = 12 + 2y + y2 + -12 + -2y + -1y2

Reorder the terms:
-12 + x2 + -2y + -1y2 = 12 + -12 + 2y + -2y + y2 + -1y2

Combine like terms: 12 + -12 = 0
-12 + x2 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2
-12 + x2 + -2y + -1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
-12 + x2 + -2y + -1y2 = 0 + y2 + -1y2
-12 + x2 + -2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-12 + x2 + -2y + -1y2 = 0

The solution to this equation could not be determined.