Solve the equation by factoring. $$ 16 x^{2}+2 x-3=0 $$ Rewrite the equation in factored form $$ (8 x-3)(2 x+1)=0 $$ (Factor completely.) The solution set is $$ \} $$ (Use a comma to separate answers as needed.

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To solve the equation $$ 16x^{2} + 2x - 3 = 0 $$ by factoring, follow these steps:

1. **Factor the quadratic equation:**

The given equation can be factored as:
   $$
   (8x - 3)(2x + 1) = 0
   $$

2. **Find the solutions by setting each factor equal to zero:**

- **First factor:**
     $$
     8x - 3 = 0 \
     8x = 3 \
     x = \frac{3}{8}
     $$
     
   - **Second factor:**
     $$
     2x + 1 = 0 \
     2x = -1 \
     x = -\frac{1}{2}
     $$

3. **Write the solution set:**

The solutions to the equation are:
   $$
   \left\{ -\frac{1}{2}, \frac{3}{8} \right\}
   $$

**Answer:**  
$$\left\{\, -\dfrac{1}{2},\; \dfrac{3}{8} \,\right\}$$
The solutions are $$ x = -\frac{1}{2} $$ and $$ x = \frac{3}{8} $$.

Solve the equation by factoring.

Rewrite the equation in factored form

(Factor completely.)
The solution set is
(Use a comma to separate answers as needed.

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Solve the equation by factoring. Rewrite the equation in factored form (Factor completely.) The solution set is (Use a comma to separate answers as needed.