Question 1163336
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<pre>

    30*(p^2-1) = 11p


This equation is EQUIVALENT to this 


    {{{30p^2 - 11p - 30}}} = 0.


Complete the square, step by step


    {{{30p^2 - 11p}}} = {{{30}}}


    {{{p^2 - (11/30)p}}} = {{{1}}}


    {{{p^2 - 2*(11/60)p + (11/60)^2}}} = {{{1 + (11/60)^2}}}


    {{{(p-11/60)^2}}} = {{{1 + 121/3600}}}


    {{{(p-11/60)^2}}} = {{{3721/3600}}}


    {{{p - 11/60}}} = +/- {{{sqrt(3721/3600)}}}


    {{{p-11/60}}} = +/- {{{61/60}}}


    p = {{{11/60}}} +/- {{{61/60}}}


The roots are  {{{p[1]}}} = {{{11/60 + 61/60}}} = {{{72/60}}} = {{{6/5}}}  and

               {{{p[2]}}} = {{{11/60 - 61/60}}} = - {{{50/60}}} = - {{{5/6}}}.


Hence, the polynomial  {{{30p^2 - 11p - 30}}}  can be factored in this way


    {{{30p^2 - 11p - 30}}} = {{{30*(p-p[1])*(p-p[2])}}} = {{{30*(p-6/5)*(p+5/6)}}} = {{{(5p-6)*(6p+5)}}}.


It is the factorization the problem wants from you.
</pre>

Solved.