To solve the equation \( 30 = -x^2 + 13x \) using factoring, we first rearrange it into standard form:
\[ -x^2 + 13x - 30 = 0 \]
Multiplying through by -1 to make the leading coefficient positive:
\[ x^2 - 13x + 30 = 0 \]
Next, we look for two numbers that multiply to \( 30 \) and add to \( -13 \). The two numbers that satisfy these conditions are \( -3 \) and \( -10 \).
Now, we can factor the quadratic equation:
\[ (x - 3)(x - 10) = 0 \]
Setting each factor equal to zero gives us the solutions:
\[ x - 3 = 0 \quad \Rightarrow \quad x = 3 \]
\[ x - 10 = 0 \quad \Rightarrow \quad x = 10 \]
Thus, the solutions are:
\[ x = 3, 10 \]
So the correct response is:
x=3,10