Final answer:
To factor the equation 5x^(3)+5x^(2)-150x, first factor out the common factor 5x, and then factor the quadratic expression inside the parentheses. The factored form of the equation is 5x(x+6)(x-5).
Step-by-step explanation:
To factor the given equation 5x^(3)+5x^(2)-150x, we can factor out the common factor of 5x:
5x(x^(2)+x-30)
Next, we can factor the quadratic expression inside the parentheses:
5x(x+6)(x-5)
Therefore, the factored form of the equation is 5x(x+6)(x-5).