2ab-a^2-b^2=0

Solution for 2ab-a^2-b^2=0 equation:

Simplifying
2ab + -1a2 + -1b2 = 0

Solving
2ab + -1a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1a + b)(a + -1b) = 0

Subproblem 1
Set the factor '(-1a + b)' equal to zero and attempt to solve:

Simplifying
-1a + b = 0

Solving
-1a + b = 0

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

Add '-1b' to each side of the equation.
-1a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
-1a + 0 = 0 + -1b
-1a = 0 + -1b
Remove the zero:
-1a = -1b

Divide each side by '-1'.
a = b

Simplifying
a = b
Subproblem 2
Set the factor '(a + -1b)' equal to zero and attempt to solve:

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Solution
a = {b, b}