Chapter 11, Problem 15GR

To determine

Solve the equation $3m^2+33m+30=0$ by factoring.

Answer to Problem 15GR

Solutions of the equation $3m^2+33m+30=0$ are $m=-5\text{and}m=-6$

Explanation of Solution

Given:

The equation: $3m^2+33m+30=0$

Concept Used:

Zero-Product Property: If we multiply two (or more) things together and the result is equal to zero, then we know that  at least one  of those things that we multiplied must also have been equal to zero.

Calculation:

Find the factor form of the equation: $3m^2+33m+30=0$

Factor form: $3m^2+33m+30=0\Rightarrow 3(m+5)(m+6)=0$

Now use zero product property:

  $\begin{array}{l}3m^2+33m+30=0\\ 3(m+5)(m+6)=0\\ 3\ne 0;m+5=0\text{and}m+6=0[\text{Zero-Product Property}]\\ m=-5\text{and}m=-6\end{array}$

Thus, Solutions of the equation $3m^2+33m+30=0$ are $m=-5\text{and}m=-6$