# How do you solve 3x^2-10x+3=0?

Jun 19, 2018

See a solution process below:

#### Explanation:

We can factor the left side of the equation as:

$\left(3 x - 1\right) \left(x - 3\right) = 0$

Now, solve each term on the left side of the equation for $0$

Solution 1:

$3 x - 1 = 0$

$3 x - 1 + \textcolor{red}{1} = 0 + \textcolor{red}{1}$

$3 x - 0 = 1$

$3 x = 1$

$\frac{3 x}{\textcolor{red}{3}} = \frac{1}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = \frac{1}{3}$

$x = \frac{1}{3}$

Solution 3:

$x - 3 = 0$

$x - 1 + \textcolor{red}{3} = 0 + \textcolor{red}{3}$

$x - 0 = 3$

$x = 3$

The Solution Set Is:

$x = \left\{\frac{1}{3} , 3\right\}$