24x^2-46x=18

24x² -46x = 18

24x² -46x -18 = 0

2*(3x+1)*(4x-9) =0

1.)   3x+1=0     =>    x = -1/3 = $${\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}$$

2.)   4x-9 = 0     =>    x = 9/4 =  $${\frac{{\mathtt{9}}}{{\mathtt{4}}}}$$

First divide through by 2 and then rewrite as  12x² - 23x - 9 = 0

 

Look for factors of 9 and 12 that when suitably combined and summed make -23.

 

(3x + 1)(4x - 9) = 12x² - 27x + 4x - 9 = 12x² - 23x - 9

 

so x = -1/3 or x = 9/4

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