Question

−4(x+5)=−4x−20 how many solutions does this equation have?

Answer 1

If you distribute the 4 on left hand side, the equation becomes

$-4x-20 = -4x-20$

As you can see, this is an identity: the left and right hand side are identical.

This means that, no matter which value for x you choose, the equation will always hold: we're basically asking "for which x values something is equal to itself?" Well, obviously always.

So, this equation has infinite solutions, every single value for x you can think of is a solution of this equation.