Question 639683

{{{x^2-4x=21}}}

{{{x^2-4x-21=0}}}.........replace {{{-4x}}} with {{{3x-7x}}}

{{{x^2+3x-7x-21=0}}}...group first two and second two terms together


{{{(x^2+3x)-(7x+21)=0}}}...factor out {{{x}}} from the first group and {{{7}}} from the second group


{{{x(x+3)-7(x+3)=0}}}

{{{(x-7)(x+3)=0}}}

now find solutions: recall, product is equal to zero if any of the factors is equal to zero

so, if

{{{(x-7)=0}}}....->.....{{{x=7}}}

or

{{{(x+3)=0}}}..->.....{{{x=-3}}}