(x-a)*(x-a)=0

Solution for (x-a)*(x-a)=0 equation:

Simplifying
(x + -1a)(x + -1a) = 0

Reorder the terms:
(-1a + x)(x + -1a) = 0

Reorder the terms:
(-1a + x)(-1a + x) = 0

Multiply (-1a + x) * (-1a + x)
(-1a * (-1a + x) + x(-1a + x)) = 0
((-1a * -1a + x * -1a) + x(-1a + x)) = 0

Reorder the terms:
((-1ax + 1a2) + x(-1a + x)) = 0
((-1ax + 1a2) + x(-1a + x)) = 0
(-1ax + 1a2 + (-1a * x + x * x)) = 0
(-1ax + 1a2 + (-1ax + x2)) = 0

Reorder the terms:
(-1ax + -1ax + 1a2 + x2) = 0

Combine like terms: -1ax + -1ax = -2ax
(-2ax + 1a2 + x2) = 0

Solving
-2ax + 1a2 + x2 = 0

Solving for variable 'a'.

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

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

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

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

Simplifying
a + -1x = 0

Solving
a + -1x = 0

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

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

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

Simplifying
a = x
Solution
a = {x, x}