Simplify to standard form?

Rearrange the terms:
3x^2+6x+y^2-8y-11=0

Add 11 to both sides and factor 3 out of the terms with x in them:
3(x^2+2x)+y^2-8y=11

Complete the square for both x and y:
3(x^2+2x+1)+(y^2-8y+16)-3-16=11

Simplify the parts inside the parentheses and add 3 and 16 to both sides:
3(x+1)^2+(y-4)^2=30

Divide both sides by 30:
(x+1)^2/10 + (y-4)^2/30+1

That's standard form for an ellipse.

3 [ x² + 2x ] + [ y² - 8y ] = 11

3 [ x² + 2x + 1 ] + [ y² - 8y + 16 ] = 27

3 [ x + 1 ]² + [ y - 4 ]² = 27

3x^2 + y^2 + 6x - 8y - 11 = 0 ... given equation
3(x^2 + 2x) + (y^2 - 8y) = 11 ... group, remove common constants
3( x^2 + 2x + 1) + (y^2 - 8y + 16) = 11 + 3 + 16 ... complete the squares
3(x+1)^2 + (y-4)^2 = 30 ... show as squares
(x+1)^2/10 + (y-4)^2/30 = 1 ... divide by 30 to get standard form