Question 728317
<pre>
x³ - 4x² - 6x = 0

Factor x out of the left side:

x(x² - 4x - 6) = 0

We use the zero factor property:

x = 0;   x² - 4x - 6 = 0

         x = {{{(-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
         x = {{{(-(-4) +- sqrt( (-4)^2-4*(1)*(-6) ))/(2*(1)) }}}
         x = {{{(4 +- sqrt(16+24 ))/2 }}}         
         x = {{{(4 +- sqrt(40 ))/2 }}}
         x = {{{(4 +- sqrt(4*10))/2 }}}
         x = {{{(4 +- 2sqrt(10))/2 }}}
         x = {{{(2(2 +- sqrt(10)))/2 }}}
         x = {{{(cross(2)(2 +- sqrt(10)))/cross(2) }}}
         x = 2±&#8730;<span style="text-decoration: overline">10</span>

So there are three solutions:

0, 2+&#8730;<span style="text-decoration: overline">10</span>, 2-&#8730;<span style="text-decoration: overline">10</span>

All have multiplicity 1, because there are the same number of
different solutions as the degree, which is 3.
 
Edwin</pre>