Final answer:
The quadratic equation 3u²−21u=0 is factored to u(3u−7)=0, and by setting each factor equal to zero, we find the two solutions u=0 and u=7.
Step-by-step explanation:
To solve for u in the quadratic equation 3u²−21u=0, we can start by factoring the common variable u out of both terms which gives us u(3u−7) = 0. By the zero product property, we can set each factor equal to zero, which gives us two separate equations: u = 0 and 3u−7 = 0.
We already have one solution from the first equation, which is u = 0. Then we solve the second equation by adding 21 to both sides, giving us 3u = 21. Finally, we divide both sides by 3 to find the other solution, which gives us u = 7.
Hence, the two solutions to the quadratic equation are u = 0 and u = 7.