Question

How do you factor 5x^2 = 10x

Answer 1

$5x^2 = 10x$ 

$5x^2-10x=10x-10x$ 

$5x^2-10x=0$ 

     Use quadratic formula 

$\quad x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}$ 

$\mathrm{For\:}\quad a=5,\:b=-10,\:c=0:\quad x_{1,\:2}=\dfrac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:5\cdot \:0}}{2\cdot \:5}$ 

$x=\dfrac{-\left(-10\right)+\sqrt{\left(-10\right)^2-4\cdot \:5\cdot \:0}}{2\cdot \:5}:\quad 2$ 

$x=\dfrac{-\left(-10\right)-\sqrt{\left(-10\right)^2-4\cdot \:5\cdot \:0}}{2\cdot \:5}:\quad 0$ 

$x=2,\:x=0$

Answer 2

To begin factoring, set the equation equal to zero - subtract 10x from each side:

5x² = 10x
5x² - 10x = 0

Next, see if you can pull out a GCF, --greatest common factor-- from both terms.  You can pull out 5x:

5x² - 10x = 0
5x(x - 2) = 0

The most you can factor the expression is 5x(x - 2) = 0.