Explanation:
(ax + b)(cx + d) = acx² + bcx + adx + bd =
= acx² + (bc + ad)x + bd
we have as actual result
6x² - x - 2
and we get a = 2
so,
acx² = 2cx² = 6x²
cx² = 3x²
c = 3
for the remaining terms we see
3b + 2d = -1
2d = -3b - 1
d = (-3b - 1)/2
bd = -2
b(-3b - 1)/2 = -2
b(-3b - 1) = -4
-3b² - b + 4 = 0
we could solve for a quadratic equation, but
bd = -2
has very limited possibilities (we assume we are dealing with integer solutions).
it means 1×-2 or -1×2
let's try b = 1
-3×1² - 1 + 4 = 0
-3 - 1 + 4 = 0 correct
so,
b = 1, d = -2
and we get
(2x + 1)(3x - 2)