# How do you solve the equation: 5w^2-5w=0?

Mar 14, 2018

Remove extra coefficients to reveal two solutions $w = 1$ and $w = 0$

#### Explanation:

There is a common factor on the left-hand side that is equal to $5 w$. If you pull that common factor you you see:

$5 w \left(w - 1\right) = 0$

Since anything multiplied by zero is zero, we can look at the two scenarios where you get 0=0:

$\left(w - 1\right) = 0 \Rightarrow \textcolor{red}{w = 1}$

$5 w = 0 \Rightarrow \textcolor{b l u e}{w = 0}$

We can also treat this like a quadratic equation, where:

$a = 5$
$b = - 5$
$c = 0$

$w = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$w = \frac{- \left(- 5\right) \pm \sqrt{{\left(- 5\right)}^{2} - 4 \left(5 \cdot 0\right)}}{2 \left(5\right)}$

$w = \frac{5 \pm \sqrt{25}}{10}$

$w = \frac{5 \pm 5}{10} \Rightarrow w = 1 , w = 0$