#8x^2 + 6x - 9#
Try # (4x + color(red)(a))(2x + color(red)(b))#
#8x^2 + (4color(red)(b) + 2color(red)(a))x + color(red)(ab)#
#implies 2a + 4b = 6# and #ab = -9#
Subbing #a = (-9)/b# into the first equation gives:
#2((-9)/b) + 4b = 6#
#4b - 18/b = 6#
#4b^2 - 18 = 6b implies 2b^2 - 3b - 9 = 0#
Use quadratic formula
#b = (3+-sqrt(81))/4 = (3+-9)/4 implies b = 3 or b = -3/2#
#a = -9/b implies a = -3 or a = 6#
#(4x - 3)(2x + 3) or (4x + 6)(2x-3/2)#