Can Someone Help me solving this equation using modulus operation?

Question

X mod(35-3*X)=0 How to find values of X?

Answer 1

We need $$35-3x$$ to divide $x$

Now as $(35-3x)=1, (35-3x)|x\iff(35-3x)|3x$

Use

$$\dfrac{3x}{35-3x}=-1+\dfrac{35}{35-3x}$$

So, we need to find integer $x$ such that $35-3x\in\{\pm1,\pm5,\pm7,\pm35\}$