value of x satisfying the equality $|x^2+8x+7|=|x^2+4x+4|+|4x+3|$ for $x\in R$ are

The correct option is C $(-2,\infty )$
As we know

$|a|+|b|=|a+b|$

$ab\ge 0$

$⟹(x^2+4x+4)(4x+3)\ge 0$

$⟹(x+2{)}^2(4x+3)\ge 0$

$⟹x\in [-\frac{3}{4},\infty )\cup${$-2$}