Question 112542
{{{(ax+b)(2x-3)=18x^2-23x+c}}}


{{{2ax^2-3ax+2bx-3b=18x^2-23x+c}}}
{{{2ax^2+(-3a+2b)x-3b=18x^2-23x+c}}}


Now we can extract some facts:

Fact 1: {{{2a=18}}}  Because the leading coefficients must be equal
Fact 2: {{{-3a+2b=-23}}}  Because the first degree term coefficients must be equal
Fact 3: {{{-3b=c}}}  Because the constant coefficients must be equal


Solving the Fact 1 equation for a gives us {{{a=9}}}.  We can use this value to solve the Fact 2 equation, thus:


{{{-3(9)+2b=-23}}}
{{{2b=-23+27}}}
{{{2b=4}}}
{{{b=2}}}


And then using our newly found value for b, we can solve the last equation:


{{{-3(2)=c}}}
{{{c=-6}}}


Check:
Does {{{(9x+2)(2x-3)=18x^2-23x-6}}}?


{{{(9x+2)(2x-3)}}}
{{{18x^2-27x+4x-6}}}
{{{18x^2-23x-6}}}, Check!


Hope this helps.