Question 61072
You can temporarily substitute u for {{{x^(-1)}}}, so rewriting the equation:
{{{3u^2 - 27u + 42 = 0}}} Start by factoring a 3.
{{{3(u^2 - 9u + 14) = 0}}} Aplying the zero product principle:
{{{u^2 - 9u + 14 = 0}}} Factor the the left side:
{{{(u - 2)(u - 7) = 0}}} Apply the zero product principle:
{{{u - 2 = 0}}} and/or {{{u - 7 = 0}}}

u = 2 and/or u = 7  Now replace the {{{x^(-1)}}} for u.

{{{x^(-1) = 2}}}
{{{1/x = 2}}}
{{{1 = 2x}}} 
{{{x = 1/2}}}
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{{{x^(-1) = 7}}}
{{{1/x = 7}}}
{{{1 = 7x}}}
{{{x = 1/7}}}