# How do you solve 9x^2 = 27x?

Jul 16, 2016

$x = 3$ and $x = 0$

#### Explanation:

We can rewrite $9 {x}^{2} = 27 x$ by subtracting $27 x$ from both sides and make it equal to $0$.

$9 {x}^{2} = 27 x$

$9 {x}^{2} - 27 x = 0$

Factoring out a $9$ and $x$ we now get

$9 x \left(x - 3\right) = 0$

We now have two separate factors, namely $9 x = 0$ and $x - 3 = 0$, so we can simply solve for $x$.

$9 x = 0 \to x = 0$

$x - 3 = 0 \to x = 3$

So our solutions are $x = 3$ and $x = 0$.

To check our answer, we can also graph $9 {x}^{2} - 27 x$.

graph{9x^2-27x [-2.82, 4.973, -1.955, 1.942]}

Jul 16, 2016

$x = 0$ or $x = 3$

#### Explanation:

$9 {x}^{2} = 27 x$ $\Leftrightarrow$

$9 {x}^{2} - 27 x = 0$ or

$9 x \left(x - 3\right) = 0$ or dividing by $9$

$x \left(x - 3\right) = 0$ i.e. either $x = 0$ or $x - 3 = 0$

Hence $x = 0$ or $x = 3$