non-unary coefficient in trinom formula

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I know that the trinomial formula for factorization when the coefficient for $x^2$ is $1$ is as follows:

$x^2 + bx + c = (x+x_1)(x+x_2)$ $s.t.:$

$x_1 + x_2 = b$ $and$ $x_1 \cdot x_2 = c$

Could anyone explain what changes when $a \neq 1$? How will this affect the factorization?

Thanks in advance =)