Answer
$x=-\frac{3}{2}$
Work Step by Step
$f(x)=4x+6$
Since we are solving for all the real values of $x$ when $f(x) = 0$, set the function $f(x)=4x+6$ equal to zero and we get the following equation:
$4x+6=0$
Now subtract 6 from both sides of the equation so that all of the constants are on the right side of the equation and all of the $x$ terms are on the left side.
$4x+6-6=0-6$
$4x=-6$
Once all of the constants are on the right and all the $x$ terms are on the left, solve for $x$ by dividing both sides by $4$.
$\frac{4x}{4}=\frac{-6}{4}$
$x=\frac{-6}{4}$
Now simplify the fraction by dividing both the numerator and denominator by 2.
$x=-\frac{3}{2}$
