Question 666451
{{{6x^3-26x^2-20x=0 }}} .....factor out {{{2x}}}

{{{2x(3x^2-13x-10)=0 }}}.....replace {{{-13x}}} with {{{2x-15x}}}

{{{2x(3x^2+2x-15x-10)=0 }}}.....group

{{{2x((3x^2+2x)-(15x+10))=0 }}}

{{{2x((3x^2+2x)-(15x+10))=0 }}} .factor out {{{x}}} from {{{3x^2+2x}}} and {{{5}}} from {{{15x+10}}}

{{{2x(x(3x+2)-5(3x+2))=0 }}}

{{{2x(x-5)(3x+2)=0 }}}...now we have factor it completely and we can find solutions by setting each factor equal to zero:


if {{{2x=0 }}}......=>.....{{{x=0}}}

if {{{(x-5)=0 }}}......=>.....{{{x=5}}}

if {{{(3x+2)=0 }}}......=>.....{{{3x=-2}}}=>.....{{{x=-2/3}}}



{{{ graph( 600, 600, -7, 7, -140, 7, 6x^3-26x^2-20x) }}}