(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 = 0
(-1 + 0 + a2) = 0
(-1 + a2) = 0

Solving
-1 + a2 = 0

Solving for variable 'a'.

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

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

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

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

Simplifying
a2 = 1

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