Question 862552
Hint:  Corresponding Positions.


Right-hand side is {{{x^2+x+bx+b=x^2+(1+b)x+b}}}.
Original left side then means {{{x^2+4x+a=x^2+(1+b)x+b}}}.
Use the hint.
Done???
"No".


Trying a little more thoroughly,
{{{x^2+4*x+a=(x+1)*(x+b)}}} was given.
{{{x^2+4x+a=x^2+x+bx+b}}}
{{{highlight_green(x^2+4x+a=x^2+(1+b)x+b)}}}.
Now, these are two equal quadratic expressions.  Both expressions are arranged in decreasing powers of x.  Coefficients in corresponding positions are equal.