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

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

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

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

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

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

Solving
a2 + b2 = 0

Solving for variable 'a'.

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

Add '-1b2' to each side of the equation.
a2 + b2 + -1b2 = 0 + -1b2

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

Simplifying
a2 = -1b2

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

The solution to this equation could not be determined.