Question 976116
In general it looks good, but I have not worked through the steps carefully all the way.


Denominator on the left member is correct in first step.


Now looking at numerator 
{{{2(2x+2)+4(x+3)}}}
{{{4x+4+4x+12}}}
{{{8x+16}}}


revise equation
{{{(8x+16)/(2x^2+8x+6)=10}}}
{{{8x+6=20x^2+80x+60}}}, and now subtract 8x and 6 from both sides.
{{{20x^2+72x+54=0}}}, so you made a mistake.
reduce.
{{{highlight(10x^2+36x+27=0)}}}


Solution formula for a general quadratic equation will bring the solution for what is x.



===continuing===


Discriminant is 216.
Factorization of {{{216=2*108=2*2*54=2*2*2*27=2*2*2*3*3*3}}}.
{{{x=(-36+- 6*sqrt(6))/20}}}

{{{highlight(x=(-18+- 3*sqrt(6))/10)}}}-----You can test to see if either of these individually will work in the original equation outlined in green.