Question

solve by factoring
${n}^{2} - 6n= 0$
Please show all work!​

Answer 1

Answer:

$n=0,\\n=6$

Step-by-step explanation:

Given $n^2-6n=0$, we can factor out an $n$ from each of the terms on the left side of the equation:

$n(n-6)=0$

Since we have two factors that multiply to zero, we can set each of them to zero and solve for $n$, because zero multiplied by anything is equal to zero. Therefore, as long as either $n$ or $n-6$ is equal to zero, the other factor can be any real number and the equation would still hold true.

Therefore, we have the following cases:

$\begin{cases}n=0,\\n-6=0\end{cases}$

Solving, we get:

$\begin{cases}n=0, n=\boxed{0}\\n-6=0, n=\boxed{6}\end{cases}$

Answer 2

$\\ \sf\longmapsto n^2-6n=0$

• Take n common

$\\ \sf\longmapsto n(n-6)=0$

Now

$\\ \sf\longmapsto n=0\:or \:(n-6)=0$

$\\ \sf\longmapsto n=0\:or \;n=6$

Hence roots of the equation are 0 and 6 .

More:-

We can solve it through Quadratic formula

$\boxed{\sf x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$