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

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

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

Reorder the terms:
(a + b)(-1b + x) = x(x + b)

Multiply (a + b) * (-1b + x)
(a(-1b + x) + b(-1b + x)) = x(x + b)
((-1b * a + x * a) + b(-1b + x)) = x(x + b)
((-1ab + ax) + b(-1b + x)) = x(x + b)
(-1ab + ax + (-1b * b + x * b)) = x(x + b)

Reorder the terms:
(-1ab + ax + (bx + -1b2)) = x(x + b)
(-1ab + ax + (bx + -1b2)) = x(x + b)
(-1ab + ax + bx + -1b2) = x(x + b)

Reorder the terms:
-1ab + ax + bx + -1b2 = x(b + x)
-1ab + ax + bx + -1b2 = (b * x + x * x)
-1ab + ax + bx + -1b2 = (bx + x2)

Add '-1bx' to each side of the equation.
-1ab + ax + bx + -1bx + -1b2 = bx + -1bx + x2

Combine like terms: bx + -1bx = 0
-1ab + ax + 0 + -1b2 = bx + -1bx + x2
-1ab + ax + -1b2 = bx + -1bx + x2

Combine like terms: bx + -1bx = 0
-1ab + ax + -1b2 = 0 + x2
-1ab + ax + -1b2 = x2

Solving
-1ab + ax + -1b2 = x2

Solving for variable 'a'.

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

Add 'b2' to each side of the equation.
-1ab + ax + -1b2 + b2 = b2 + x2

Combine like terms: -1b2 + b2 = 0
-1ab + ax + 0 = b2 + x2
-1ab + ax = b2 + x2

Reorder the terms:
-1ab + ax + -1b2 + -1x2 = b2 + -1b2 + x2 + -1x2

Combine like terms: b2 + -1b2 = 0
-1ab + ax + -1b2 + -1x2 = 0 + x2 + -1x2
-1ab + ax + -1b2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1ab + ax + -1b2 + -1x2 = 0

The solution to this equation could not be determined.