Answer
$x=6, -3$
Work Step by Step
$f(x)=x^2+2x+1$ and $g(x)=5x+19$
Since we are solving for all the values of $x$ when $f(x) = g(x)$, set the function $f(x)=x^2+2x+1$ equal to $g(x)=5x+19$ and we get the following equation:
$x^2+2x+1=5x+19$
Subtract $5x+19$ from both sides of the equation so that all the terms are on the left side:
$x^2+2x+1-(5x+19)=5x+19-(5x+19)$
$x^2+2x+1-5x-19=0$
$x^2-3x-18=0$
Then, factor the left side of the equation. To do this, we need to find two numbers that multiply to get -18 and add to get -3. Those numbers are -6 and 3.
$(x-6)(x+3)=0$
Next, you can see that the above equation holds true when $x-6=0$ or $x+3=0$. Solve for $x$ in each equation individually as shown below:
$x-6=0$
Add 6 to both sides.
$x-6+6=0+6$
$x=6$
Now for the other equation:
$x+3=0$
Subtract 3 from both sides of the equation:
$x+3-3=0-3$
$x=-3$
So, the solution is $x=6, -3$
