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Factorising starts by extracting the highest common factor of all the coefficients, then splits what remains into linear brackets using its roots when the discriminant is non-negative.
Factorising
ax² + bx + c = g·A(x − r₁)(x − r₂) where g = gcd(a, b, c)
The common factor 3 gives 3(2x² + 5x + 3), and the roots −1 and −1.5 give 3·2(x + 1)(x + 1.5) = 3(2x + 3)(x + 1).
Only the common factor can be taken out; the quadratic part is irreducible over the real numbers.