Question 18338
Find the value of c that will make {{{2xy-6x+c}}} factorable.

Try factoring by grouping.

{{{(2xy-6x) + (7y+c)}}} Factor 2x from the left set of parentheses.
{{{2x(y-3) + (7y+c)}}}  Factor a 7 from the second set of parentheses.
{{{2x(y-3) + 7(y+c/7)}}} Now set {{{(y+c/7) = (y-3)}}} and solve for c.

{{{y+c/7 = y-3}}} Subtract y from both sides. 
{{{c/7 = -3}}} Multiply both sides by 7.
{{{c = -21}}}

Answer: c = -21

Check: Factor by grouping;

{{{(2xy-6x)+(7y-21) = 2x(y-3) + 7(y-3)}}} = {{{(2x+7)(y-3)}}}