# How do you solve the equation for x^2 - 3x = 0?

Apr 8, 2015

${x}^{2} - 3 x = 0$

$x \cdot \left(x - 3\right) = 0$ ($x$ was a common factor to both the terms)

In general, if $a \cdot b = 0 ,$ then either $a = 0 \mathmr{and} b = 0$

So here,
$x = 0 \mathmr{and} x - 3 = 0$
 color(green)( x = 0 or x = 3 is the correct Solution.

color(red)(Note :

Here's a classic color(red)(Mistake that many students make:

Transpose $3 x$ to the right hand side

${x}^{2} = 3 x$

Divide both sides by $x$ will give us $x = 3$ (Incorrect/Incomplete)

This is a color(red)(mistake because we CANNOT divide by $x$ unless we are sure about it not being equal to zero.

Apr 8, 2015

To find $x$, we first have to factorize the equation.
${x}^{2} - 3 x = 0$
As $x$ is the common factor between the 2 values, we factorize the equation by taking $x$ out of ${x}^{2} - 3 x = 0$

${x}^{2} - 3 x = 0$
$x \left(x - 3\right) = 0$

Any value that is multiplied by 0, will give 0 as the answer.
1x0=0
2x0=0
3x0=0

From here, we know that in $x \left(x - 3\right) = 0$,
$x = 0$ and $\left(x - 3\right) = 0$

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

Therefore $x = 0$ and $x = 3$