Answer
The number is $-22$.
Work Step by Step
Let $x$ be the unknown number.
Then, the sum of a number and $15$ is $x+15$.
Translating $``\text{six times the sum of a number and 15}"$ yields $6(x+15)$.
Thus, the equation needed to find the unknown number is:
$$6(x+15)=-42$$
Solve the equation:
$$\begin{align*}
\frac{6(x+15)}{6}&=\frac{-42}{6} &\text{Divide 6 to both sides.}\\
x+15&=-7 &\text{Simplify.}\\
x+15-15&=-7-15 &\text{Subtract 15 from each side.}\\
x&=-22 &\text{Simplify.}
\end{align*}$$
Thus, the number is $-22$.
