# How do you solve 10u^3-5u^2=0?

Jun 2, 2016

$u ' = 0 , u ' ' = 0 , u ' ' ' = \frac{1}{2}$

#### Explanation:

This is a third degree equation without and independent term, therefore it can be solve though factorization. Start by factoring u:

$u \left(10 {u}^{2} - 5 u\right) = 0$.

Notice that, for this new equation to result in 0, any of the factors must me 0. If the first $u$ is zero, then we have found one answer: $u ' = 0$.

However, if $10 {u}^{2} - 5 u = 0$, then we must factor the equation again to solve it:

$u \left(10 u - 5\right) = 0$.

Again, we have a case in which the first $u$ can be zero, so:
$u ' ' = 0$.

Now, if $10 u - 5 = 0$, then:
$10 u = 5$
$u ' ' ' = \frac{5}{10} = \frac{1}{2}$.

Do notice that this method only works when the equation is equals zero and there is no independent term. We could also have taken a shortcut and factored ${u}^{2} \left(10 u - 5\right)$ right from the beginning, since we have two identical answers and the original equation does not have ${u}^{1}$.