Algebra

We could probably do this really hard way. 

By distributing every number, we get

${x^{3}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x^{2}\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+x\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)+1\left(x^{4}+3x^{3}+4x^{2}+8x+7\right)}$

Simplfying, we have

$x^{7}+4x^{6}+8x^{5}+16x^{4}+22x^{3}+19x^{2}+15x+7$

As it clear shows$15$ is the coefficient of x. 

So our final answer is 15. 

Thanks! :)