Modular Equation Solving | x2 + 8x ≡ 0 (mod 56) | Step-by-Step Guide

[Cheesycheese213]

Homework Statement

Solve the modular equation x² + 8x ≡ 0 (mod 56)

Homework Equations

Let a, b = integer
n|(a - b), written as a ≡ b (mod n)

The Attempt at a Solution

I tried to separate them, and got
2|x² + 8x or x² + 8x ≡ 0 (mod 2) as well as
7|x² + 8x or x² + 8x ≡ 0 (mod 7)
but I'm a bit stuck now, and I'm pretty sure they might be wrong?

How should I be solving this? Thanks!

 

[Mark44]

Homework Statement

Solve the modular equation x² + 8x ≡ 0 (mod 56)

Homework Equations

Let a, b = integer
n|(a - b), written as a ≡ b (mod n)

The Attempt at a Solution

I tried to separate them, and got
2|x² + 8x or x² + 8x ≡ 0 (mod 2) as well as
7|x² + 8x or x² + 8x ≡ 0 (mod 7)
but I'm a bit stuck now, and I'm pretty sure they might be wrong?

How should I be solving this? Thanks!

Can't you write the original equation as $x(x + 8) \equiv 0 \mod 56$?