Question

solve for u.
$6u^2 - 24u = 0$
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
u =

Explanation:

Step1: Factor out the GCF

We start with the equation \(6u^{2}-24u = 0\). The greatest common factor (GCF) of \(6u^{2}\) and \(-24u\) is \(6u\). Factoring out \(6u\), we get:
\(6u(u - 4)=0\)

Step2: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For the equation \(6u(u - 4)=0\), we set each factor equal to zero:

• Case 1: \(6u=0\)

Dividing both sides of the equation \(6u = 0\) by \(6\), we have \(u=\frac{0}{6}=0\).

• Case 2: \(u - 4=0\)

Adding \(4\) to both sides of the equation \(u - 4=0\), we get \(u=4\).

Answer:

\(0,4\)