Question

solve $7n^2 = 35n$
$n = \square$, $n = \square$

Explanation:

Step1: Move all terms to one side

Subtract \(35n\) from both sides to get \(7n^2 - 35n = 0\).

Step2: Factor out the common term

Factor out \(7n\) from the left - hand side: \(7n(n - 5)=0\).

Step3: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \(7n(n - 5)=0\), we have two cases:
Case 1: \(7n=0\), dividing both sides by 7 gives \(n = 0\).
Case 2: \(n - 5=0\), adding 5 to both sides gives \(n = 5\).

Answer:

\(n = 0\), \(n = 5\)