# How do you factor 16x^2=56x?

Jul 1, 2015

$8 x \left(2 x - 7\right) = 0$

#### Explanation:

We will move the right-hand side to the left-hand side :

$16 {x}^{2} = 56 x$ <=> $16 {x}^{2} - 56 x = 0$

After that, we have to find the common factor inside the subtraction :

$16 {x}^{2} = \textcolor{red}{2 \cdot 2 \cdot 2} \cdot 2 \cdot x \cdot \textcolor{g r e e n}{x}$ and $56 x = \textcolor{red}{2 \cdot 2 \cdot 2} \cdot 7 \cdot \textcolor{g r e e n}{x}$

Then the common factor of $16 {x}^{2}$ and $56 x$ is $\textcolor{red}{2 \cdot 2 \cdot 2} \cdot \textcolor{g r e e n}{x} = 8 x$ and so : $16 {x}^{2} = 8 x \cdot 2 x$ and $56 x = 8 x \cdot 7$

Therefore, the factorization of $16 {x}^{2} - 56 x = 0$ is :
$8 x \cdot 2 x - 8 x \cdot 7 = 0$ <=> $8 x . \left(2 x - 7\right) = 0$

And now you can solve this equation with the property of multiplication!