3(2) + 24x + 48 = 0
6 + 24x + 48 = 0
24x + 54 = 0
24x + 54 - 54 = 0 - 54
24x = -54
24x/24 = -54/24
x = -9/4
x = -2 1/4
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The terms in x in the factorisation must be 3 and 1, the whole numbers must be factors of 48 ie 1/48, 2/24, 3/16, 4/12, or 6/8. The only ones which can combine with the 3 to give a sum of 24 are 4 and 12 viz: (3x + 12)(x + 4)
3x + 10x - 48 = 0 13x = 48 x = 3.692307692
3x+12=x+48: 3x-x=-12+48 2x=36 x=18
x² + 8x - 48 = (x + 12)(x - 4) x² + 8x + 48 = (4+(√32)i)(4-(√32)i)
8r + 17 = 65 8r = 65 - 17 8r = 48 r = 48 / 8 r = 6