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

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

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

Multiply k * z
kz = z(z + -3)(z + 1)

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

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

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

Combine like terms: -3z + 1z = -2z
kz = z(-3 + -2z + z2)
kz = (-3 * z + -2z * z + z2 * z)
kz = (-3z + -2z2 + z3)

Solving
kz = -3z + -2z2 + z3

Solving for variable 'k'.

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

Divide each side by 'z'.
k = -3 + -2z + z2

Simplifying
k = -3 + -2z + z2