```Question 166426
you are absolutely correct in setting up your equation.  Good job!
Now you just need to do the math to find out what x is.
.
Left side
x+x+2=2+2x
.
Right side
you need to foil (x+2)(x+4) and then distribute the {{{1/4}}} throughout all the terms.
{{{(1/4)(x*x+x*4+2*x+2*4)}}}
=
{{{(1/4)(x^2+4x+2x+8)}}}
combine like terms
{{{(1/4)(x^2+6x+8)}}}
.
distribute
{{{(x^2+6x+8)/4}}}
so you have
left side = right side
{{{2+2x=(x^2+6x+8)/4}}}
get rid of the 4 in the denominator by multiplying everything on the left and right side by 4.
{{{8+8x=(x^2+6x+8)}}}
get everything on one side
subtract (8+8x) from each side  *make sure you use parenthesis() so you subtract both terms
{{{0=x^2+6x+8-(8+8x)}}}
distribute the negative
{{{0=x^2+6x+8-8-8x}}}
combine like terms
{{{0=x^2-2x}}}
.
factor out an x
{{{0=x(x-2)}}}
x=0;
x=2
either one of these will work but since 0 is neither even or odd you can not use x=0 therefore x=2.
.
So, your three consecutive even integers are x, x+2, x+4 or 2,4,6
.
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