Question

Solve:$18a^2-30=-33a$

Short answer

The solution is$a=\frac{2}{3},-\frac{5}{2}$.

Step-by-step solution

Step 1. Given Information.

The given equation is$18a^2-30=-33a$.

Step 2. Factor the equation.

Factor the greatest common factor,

$$\begin{gathered} 18a^2-30=-33a \\ 18a^2+33a-30=0 \\ 3(6a^2+11a-10)=0 \end{gathered}$$

Now, Factor the trinomial,

$$\begin{gathered} 3(6a^2+15a-4a-10)=0 \\ 3\left\{3a\right(2a+50-2(2a+5)\}=0 \\ 3(3a-2\left)\right(2a+5)=0 \end{gathered}$$

Step 3. Solution of the equation.

Use the Zero Product Property that is set each factor to $0$.

Therefore,

$$\begin{gathered} 3a-2=0 \\ a=\frac{2}{3} \\ 2a+5=0 \\ a=-\frac{5}{2} \end{gathered}$$