The answer is infinitely many.
The -7 appearing in both sides can be canceled by adding 7 to both sides. Also, -4x+10x in the left hand sides results into 6x. We remain with
which is an identity, and as such has infinitely many solutions. In fact, an indentity has equal left and right hand side. So, the equation sounds like "for which value(s) of x does something equal itself?". This should make clear that the answer is "something is always equal to itself, no matter what the value of x is".
And since the value of x doesn't matter, you can plug any value you like, and the equation will always be true.