Code:

import sympy

x, m = sympy.symbols('x m')
eq = x**2 - 2*m*x - m - 3

# Substitute x = -1 to find m
m_val = sympy.solve(eq.subs(x, -1), m)[0]

# Substitute m back into the equation
final_eq = eq.subs(m, m_val)

# Find roots
roots = sympy.solve(final_eq, x)

# Identify the other root
other_root = [r for r in roots if r != -1][0]

print(f"{m_val=}")
print(f"{final_eq=}")
print(f"{roots=}")
print(f"{other_root=}")

Output:

m_val=2
final_eq=x**2 - 4*x - 5
roots=[-1, 5]
other_root=5