(q-1)(q+1)=0

Solution for (q-1)(q+1)=0 equation:

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

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

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

Multiply (-1 + q) * (1 + q)
(-1(1 + q) + q(1 + q)) = 0
((1 * -1 + q * -1) + q(1 + q)) = 0
((-1 + -1q) + q(1 + q)) = 0
(-1 + -1q + (1 * q + q * q)) = 0
(-1 + -1q + (1q + q2)) = 0

Combine like terms: -1q + 1q = 0
(-1 + 0 + q2) = 0
(-1 + q2) = 0

Solving
-1 + q2 = 0

Solving for variable 'q'.

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

Add '1' to each side of the equation.
-1 + 1 + q2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + q2 = 0 + 1
q2 = 0 + 1

Combine like terms: 0 + 1 = 1
q2 = 1

Simplifying
q2 = 1

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