(a+b)x(a-b)=5

Solution for (a+b)x(a-b)=5 equation:

Simplifying
(a + b) * x(a + -1b) = 5

Reorder the terms for easier multiplication:
x(a + b)(a + -1b) = 5

Multiply (a + b) * (a + -1b)
x(a(a + -1b) + b(a + -1b)) = 5
x((a * a + -1b * a) + b(a + -1b)) = 5

Reorder the terms:
x((-1ab + a2) + b(a + -1b)) = 5
x((-1ab + a2) + b(a + -1b)) = 5
x(-1ab + a2 + (a * b + -1b * b)) = 5
x(-1ab + a2 + (ab + -1b2)) = 5

Reorder the terms:
x(-1ab + ab + a2 + -1b2) = 5

Combine like terms: -1ab + ab = 0
x(0 + a2 + -1b2) = 5
x(a2 + -1b2) = 5
(a2 * x + -1b2 * x) = 5
(a2x + -1b2x) = 5

Solving
a2x + -1b2x = 5

Solving for variable 'a'.

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

Add 'b2x' to each side of the equation.
a2x + -1b2x + b2x = 5 + b2x

Combine like terms: -1b2x + b2x = 0
a2x + 0 = 5 + b2x
a2x = 5 + b2x

Divide each side by 'x'.
a2 = 5x-1 + b2

Simplifying
a2 = 5x-1 + b2

Reorder the terms:
a2 = b2 + 5x-1

Reorder the terms:
a2 + -1b2 + -5x-1 = b2 + -1b2 + 5x-1 + -5x-1

Combine like terms: b2 + -1b2 = 0
a2 + -1b2 + -5x-1 = 0 + 5x-1 + -5x-1
a2 + -1b2 + -5x-1 = 5x-1 + -5x-1

Combine like terms: 5x-1 + -5x-1 = 0
a2 + -1b2 + -5x-1 = 0

The solution to this equation could not be determined.