Solve the equation. Express numbers in exact simplest form. $$ r(r+11)(6 r+5)=0 $$ The solution set is $$ \{\square\} $$.

Question

UpStudy AI · Accepted Answer

We start with the equation
$$
r(r+11)(6r+5)=0.
$$
Since the product is zero, we set each factor equal to zero.

1. For the first factor:
   $$
   r=0.
   $$

2. For the second factor:
   $$
   r+11=0 \quad \Longrightarrow \quad r=-11.
   $$

3. For the third factor:
   $$
   6r+5=0 \quad \Longrightarrow \quad 6r=-5 \quad \Longrightarrow \quad r=-\frac{5}{6}.
   $$

Thus, the solution set is
$$
\{0,\ -11,\ -\frac{5}{6}\}.
$$
The solutions are $$ r = 0 $$, $$ r = -11 $$, and $$ r = -\frac{5}{6} $$.

Solve the equation. Express numbers in exact simplest form. \[ r(r+11)(6 r+5)=0 \] The solution set is \( \{\square\} \).