Question 86473
The first question is factor on grouping: 


{{{18a^3 - 24a^2b + 15ab^2 - 20b^3}}} 


Between the first two terms we find {{{6a^2}}} as the common factor and the next two terms we find {{{5b^2}}} as a common factor. 


Hence, the above equation can be written as: 


{{{(6a^2 (3a - 4b)) + (5b^2(3a - 4b))}}} 


Here we observe that (3a - 4b) is a common factor between the terms. 


{{{ (3a - 4b)(6a^2 + 5b^2)}}} 


Thus, the solution. 


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The second Probelm is to factorize  the given quadratic equation. 


The given expression is: 


{{{18x^2 + 9x - 2 = 0}}}


==> The middle terms can be factored as +12x and a -3x which when multiplied gives us {{{-36x^2}}} 


Hence, this can be written as: 


{{{18x^2 + 12x - 3x - 2 = 0 }}} 


{{{6x(3x + 2)- 1(3x + 2) = 0 }}}


==> (3x + 2)(6x - 1) = 0 


==> Which implies that either of them is equal to zero. 


(3x + 2) = 0  OR (6x - 1) = 0


==> 3x = - 2 OR 6x = 1


==> {{{x = (-2/3)}}} OR x = {{{(1/6)}}}


Hence, the solution. 


Regards