a(x*a)=b(x-b)

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

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

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

Multiply a * ax
a2x = b(x + -1b)

Reorder the terms:
a2x = b(-1b + x)
a2x = (-1b * b + x * b)

Reorder the terms:
a2x = (bx + -1b2)
a2x = (bx + -1b2)

Solving
a2x = bx + -1b2

Solving for variable 'a'.

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

Divide each side by 'x'.
a2 = b + -1b2x-1

Simplifying
a2 = b + -1b2x-1

Reorder the terms:
a2 + -1b + b2x-1 = b + -1b + -1b2x-1 + b2x-1

Combine like terms: b + -1b = 0
a2 + -1b + b2x-1 = 0 + -1b2x-1 + b2x-1
a2 + -1b + b2x-1 = -1b2x-1 + b2x-1

Combine like terms: -1b2x-1 + b2x-1 = 0
a2 + -1b + b2x-1 = 0

The solution to this equation could not be determined.