Question 310702
Break up the number line into 4 regions,
Region {{{1}}}: ({{{-infinity}}},{{{-14}}})
Region {{{2}}}: ({{{-14}}},{{{-2}}})
Region {{{3}}}: ({{{-2}}},{{{1}}})
Region {{{4}}}: ({{{1}}},{{{infinity}}})
Pick a point in each region (not the endpoints) and test the inequality.
If the inequality is true, that region is part of the solution set.
.
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Region {{{1}}}, let {{{x=-20}}}
 {{{ (x+14)(x-1)(x+2)>0}}}
 {{{ (-20+14)(-20-1)(-20+2)>0}}}
 {{{(-6)(-21)(-18)>0}}}
{{{-2268>0}}}
False
.
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Region {{{2}}}, let {{{x=-10}}}
 {{{ (x+14)(x-1)(x+2)>0}}}
 {{{(-10+14)(-10-1)(-10+2)>0}}}
 {{{(4)(-11)(-8)>0}}}
{{{352>0}}}
True
.
.
Region {{{3}}}, let {{{x=0}}}
 {{{ (x+14)(x-1)(x+2)>0}}}
 {{{(14)(-1)(2)>0}}}
{{{ -28>0}}}
False
.
.
Region {{{4}}}, let {{{x=2}}}
 {{{ (x+14)(x-1)(x+2)>0}}}
 {{{(2+14)(2-1)(2+2)>0}}}
 {{{(16)(1)(4)>0}}}
{{{64>0 }}}
True
So then the solution includes Regions 2 and 4.
({{{-14}}},{{{-2}}})U({{{1}}},{{{infinity}}})