Question content area topPart 1Solve the equation by​ factoring, using​ tables, or by graphing.8vsquaredminus18vplus9equals0Question content area bottomPart 1vequalsenter your response here​(Type an integer or a simplified fraction. Use a comma to separate answers as​ needed.)

To solve the equation \( 8v^2 - 18v + 9 = 0 \), we can use the factoring method.

First, let's look for two numbers that multiply to \( 8 \times 9 = 72 \) and add up to \( -18 \).

The factoring approach will involve rewriting the equation in the form:

\[ (Av + B)(Cv + D) = 0 \]

where \( A \times C = 8 \) and \( B \times D = 9 \).

After checking different combinations, we can factor the quadratic:

Rewrite the equation:

\[ 8v^2 - 12v - 6v + 9 = 0 \]

Group the terms:

\[ (8v^2 - 12v) + (-6v + 9) = 0 \]

Factoring each group yields:

\[ 4v(2v - 3) - 3(2v - 3) = 0 \]

Now, factor out the common factor \( (2v - 3) \):

\[ (4v - 3)(2v - 3) = 0 \]

Setting each factor to zero gives us the possible values for \( v \):

1. \( 4v - 3 = 0 \) \[ 4v = 3 \] \[ v = \frac{3}{4} \]

2. \( 2v - 3 = 0 \) \[ 2v = 3 \] \[ v = \frac{3}{2} \]

Thus, the solutions to the equation \( 8v^2 - 18v + 9 = 0 \) are:

\[ v = \frac{3}{4}, \frac{3}{2} \]

So the final answer is:

\[ v = \frac{3}{4}, \frac{3}{2} \]