a(a+b)-b(a+b)=0

Solution for a(a+b)-b(a+b)=0 equation:

Simplifying
a(a + b) + -1b(a + b) = 0
(a * a + b * a) + -1b(a + b) = 0

Reorder the terms:
(ab + a2) + -1b(a + b) = 0
(ab + a2) + -1b(a + b) = 0
ab + a2 + (a * -1b + b * -1b) = 0
ab + a2 + (-1ab + -1b2) = 0

Reorder the terms:
ab + -1ab + a2 + -1b2 = 0

Combine like terms: ab + -1ab = 0
0 + a2 + -1b2 = 0
a2 + -1b2 = 0

Solving
a2 + -1b2 = 0

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.
a2 + -1b2 + b2 = 0 + b2

Combine like terms: -1b2 + b2 = 0
a2 + 0 = 0 + b2
a2 = 0 + b2
Remove the zero:
a2 = b2

Simplifying
a2 = b2

Take the square root of each side:
a = {-1b, b}