(z+1)(z-1)=3

Solution for (z+1)(z-1)=3 equation:

Simplifying
(z + 1)(z + -1) = 3

Reorder the terms:
(1 + z)(z + -1) = 3

Reorder the terms:
(1 + z)(-1 + z) = 3

Multiply (1 + z) * (-1 + z)
(1(-1 + z) + z(-1 + z)) = 3
((-1 * 1 + z * 1) + z(-1 + z)) = 3
((-1 + 1z) + z(-1 + z)) = 3
(-1 + 1z + (-1 * z + z * z)) = 3
(-1 + 1z + (-1z + z2)) = 3

Combine like terms: 1z + -1z = 0
(-1 + 0 + z2) = 3
(-1 + z2) = 3

Solving
-1 + z2 = 3

Solving for variable 'z'.

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

Add '1' to each side of the equation.
-1 + 1 + z2 = 3 + 1

Combine like terms: -1 + 1 = 0
0 + z2 = 3 + 1
z2 = 3 + 1

Combine like terms: 3 + 1 = 4
z2 = 4

Simplifying
z2 = 4

Take the square root of each side:
z = {-2, 2}