Question

solve the equation.

\\(2x - 5)(6x + 5) = 0\\

\\(x = \square\\)

(simplify your answer. type each solution only once. use a comma to separate answers as needed.)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Apply the Zero Product Property

$$ (2x - 5)(6x + 5) = 0 $$

$$ 2x - 5 = 0 \quad \text{or} \quad 6x + 5 = 0 $$

Step 2: Solve the first equation

$$ 2x - 5 = 0 $$

$$ 2x = 5 $$

$$ x = \frac{5}{2} $$

Step 3: Solve the second equation

$$ 6x + 5 = 0 $$

$$ 6x = -5 $$

$$ x = -\frac{5}{6} $$

Answer:

$$ x = \frac{5}{2}, -\frac{5}{6} $$