Question

What is the integer solution of `6x^2+9=21x`?

Answer 1

Re-arrange `6x^2+9 = 21x`
into the more usual form
`6x^2-21x+9 = 0`

then factor the left hand side
`(6x-3)(x-3)=0`

which implies
either `(6x-3)=0` ...but this does not have an integer solution
or `(x-3) = 0` ...which has an integer solution `x=3`

The only integer solution to `6x^2+9=21x` is `x=3`