Question 443756
{{{ 6x^2+12x+6 }}}
Divide both sides by {{{6}}}
{{{ x^2 + 2x + 1 = 0 }}}
Use the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 1}}}
{{{b = 2}}}
{{{c = 1}}}
{{{x = (-2 +- sqrt( 2^2 - 4*1*1 ))/(2*1) }}}
{{{x = (-2 +- sqrt( 4 - 4 )) / 2 }}}
{{{x = (-2) / 2 }}}
{{{ x = -1 }}}
This is called a double root, since the 
equation must have 2 roots, it has the same
root twice. Plug it back in for {{{x}}} to check.
Rewrite it as:
{{{ x + 1 = 0 }}} 1st factor
{{{ x + 1 = 0 }}} 2nd factor
{{{ (x + 1)^2 = 0 }}} answer
Note that after you multiply it out as
{{{ x^2 + 2x + 1 = 0}}}
Multiplying both sides by {{{6}}} doesn't change anything