What are all solutions of equation f(-3x)=0 if the roots of equation f(x)=0 are -1 and -2?

Since the equation f(x) = 0 has two roots, then the
equation is a quadratic:

f(x) =
(x+1)(x+2)

f(x) = x^2 + 3x +
2

f(-3x) = (-3x)^2 + 3*(-3x) +
2

f(-3x) = 9x^2 - 9x + 2

We'll
apply quadratic formula:

x1 = [9+sqrt(81 -
72)]/18

x1 = (9+3)/18

x1 =
12/18

x1 = 2/3

x2 =
(9-3)/18

x2 = 6/18

x2 =
1/3

Another way to solve the problem is to consider that
any root of an equation, substituted within equation, verifies
it.

f(-1) = 0

But f(-3x) =
0

f(-3x) = f(-3*(1/3)) = f(-1) = 0 => x =
1/3

f(-3x) = f(-3*(2/3)) = f(-2) = 0 => x =
2/3

Therefore, the solutions of the quadratic
equation f(-3x)=0 are {1/3 ; 2/3}.