(a-1)(a-1)=0

Solution for (a-1)(a-1)=0 equation:

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

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

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

Multiply (-1 + a) * (-1 + a)
(-1(-1 + a) + a(-1 + a)) = 0
((-1 * -1 + a * -1) + a(-1 + a)) = 0
((1 + -1a) + a(-1 + a)) = 0
(1 + -1a + (-1 * a + a * a)) = 0
(1 + -1a + (-1a + a2)) = 0

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

Solving
1 + -2a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1a = 0 + -1
-1a = 0 + -1

Combine like terms: 0 + -1 = -1
-1a = -1

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

Simplifying
a = 1
Solution
a = {1, 1}