Questions: Find the real solutions by factoring. 5 x^3 = 8 x^2 What is the solution set? Select the correct choice below A. B. There are no solutions.

Solution Steps

Start by moving all terms to one side of the equation to set it equal to zero: \[ 5x^{3} - 8x^{2} = 0 \]

Factor out the greatest common factor, which is \( x^{2} \): \[ x^{2}(5x - 8) = 0 \]

Set each factor equal to zero and solve for \( x \):

1. \( x^{2} = 0 \)
   \( x = 0 \)

2. \( 5x - 8 = 0 \)
   \( 5x = 8 \)
   \( x = \frac{8}{5} \)

The solution set is \( \boxed{0, \frac{8}{5}} \).

Final Answer