Solve the equation. $$ 2^{x^{2}-72}=4^{3 x} $$ The solution set is (Use a comma to separate answers as needed.)

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We start with the equation:
$$
2^{x^{2}-72} = 4^{3x}.
$$
Since $$4 = 2^2$$, we can rewrite the right-hand side:
$$
4^{3x} = (2^2)^{3x} = 2^{6x}.
$$
Now the equation becomes:
$$
2^{x^{2}-72} = 2^{6x}.
$$
Since the bases are equal, the exponents must be equal:
$$
x^{2} - 72 = 6x.
$$
Rearrange the equation into a standard quadratic form:
$$
x^{2} - 6x - 72 = 0.
$$
Next, factor the quadratic:
$$
(x - 12)(x + 6) = 0.
$$
Setting each factor equal to zero gives:
$$
x - 12 = 0 \quad \text{or} \quad x + 6 = 0.
$$
Thus, the solutions are:
$$
x = 12 \quad \text{or} \quad x = -6.
$$
The solution set is: $$12, -6$$.
The solutions are $$ x = 12 $$ and $$ x = -6 $$.

Solve the equation.

The solution set is
(Use a comma to separate answers as needed.)

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Solve the equation. The solution set is (Use a comma to separate answers as needed.)