6) \( 4 x^{2}=16 x \)

To solve the equation \( 4x^{2} = 16x \), start by moving all terms to one side so that the equation becomes \( 4x^{2} - 16x = 0 \). Next, factor out the common term, which gives \( 4x(x - 4) = 0 \). This implies either \( 4x = 0 \) or \( x - 4 = 0 \). Solving these equations gives \( x = 0 \) or \( x = 4 \) as the solutions. Now, let’s explore how this quadratic equation can often pop up in the world of finance, particularly in calculating profit margins or breaking even points. Say you have a company producing toys, and your revenue and costs can be modeled by a quadratic equation like ours. Finding the points where profit equals zero can help decide if you need to tweak your production strategy!