Find the product of the values of $x$ that satisfy the equation $|4x|+3=35$.
I can start by subtracting 3 from both sides to get $|4x|=32$. Now, to remove the absolute value, I need to consider two cases: either 4x is positive or negative. If 4x is positive, then $|4x|=4x$ and I can divide both sides by 4 to get $x=8$. If 4x is negative, then $|4x|=-4x$ and I can divide both sides by -4 to get $x=-8$. So, the values of $x$ that satisfy the equation are 8 and -8. To find their product, I just multiply them together: $8\times -8=-64$. 