The tangent is a line of slope "m".

The derivative of the function gives this slope.

As the tangent passes through the origin, it's equation is y=mx, as c=0.

Hence, the point of intersection of this tangent and the curve gives us x.

The equation of the tangent(s) through (0,0) is

Solving f(x) for the curve = mx for the line finds x.

Solving this, bearing in mind that x=-4 is not part of the domain of f(x) or f'(x) discovers x.

Hence multiply both fractions by (x+4) before solving for x.