Question 1040243
{{{(ax-3)(bx+6)=24x^2+cx-18}}}
{{{abx^2-3bx+6ax-18=24x^2+cx-18}}}
{{{abx^2+(6a-3b)x-18=24x^2+cx-18}}}
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{{{system(ab=24,6a-3b=c)}}} and given {{{a+b=10}}}.


Question is, what can be c?
Observe, three equations and three unknown variables.
{{{system(ab=24,6a-3b=c,a+b=10)}}}.


TWO of the equations are only in the two unknowns a and b.
b=10-a
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{{{a(10-a)=24}}}
{{{10a-a^2=24}}}
{{{-a^2+10a-24=0}}}
{{{a^2-10a+24=0}}}
{{{(a-4)(a-6)=0}}}
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Possible, {{{system(a=4,or,a=6)}}}
Correspondingly, {{{system(b=6,or,b=4)}}}


Possible c values:
{{{c=6a-3b}}} as already found,
{{{c=6*4-3*6=highlight(6)}}}
or
{{{c=6*6-3*4=36-12=highlight(24)}}}