Answer
$x=2$ and $x=3$
Work Step by Step
We are given that $x^{2}+6=5x$. We can first subtract 5x from both sides of the equation to get all terms on one side.
$x^{2}-5x+6=0$
We know that 2 and 3 are factors of six and the sum of -2 and -3 is equal to $-2+(-3)=-5$ (which is the coefficient attached to the middle term). Therefore, we can factor the existing polynomial into $(x-2)(x-3)=0$
Set both terms in parentheses equal to 0.
$x-2=0$
Add 2 to both sides.
$x=2$
$x-3=0$
Add 3 to both sides.
$x=3$
