Solve by factoring.3wsquaredminus10wequals8Question content area bottomPart 1Select the correct choice and fill in any answer boxes in your choice below.A.wequalsenter your response here​(Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as​ needed.)B.The solution is not a real number.

Answer 1

To solve the equation \( 3w^2 - 10w = 8 \) by factoring, we'll first bring all terms to one side to set the equation to zero:

\[ 3w^2 - 10w - 8 = 0 \]

Next, we'll factor the quadratic equation. We need to find two numbers that multiply to \( 3 \times -8 = -24 \) and add to \(-10\).

The two numbers that meet these criteria are \(-12\) and \(2\) because:

\(-12 + 2 = -10\) and \(-12 \times 2 = -24\).

Now, we can rewrite the quadratic as:

\[ 3w^2 - 12w + 2w - 8 = 0 \]

Now, group the terms:

\[ (3w^2 - 12w) + (2w - 8) = 0 \]

Factor by grouping:

\[ 3w(w - 4) + 2(w - 4) = 0 \]

Now factor out the common factor \((w - 4)\):

\[ (w - 4)(3w + 2) = 0 \]

Now we can set each factor to zero:

1. \( w - 4 = 0 \)

   • \( w = 4 \)

2. \( 3w + 2 = 0 \)

   • \( 3w = -2 \)
   • \( w = -\frac{2}{3} \)

Thus, the solutions are:

\[ w = 4 \quad \text{and} \quad w = -\frac{2}{3} \]

So the final answer is:

A. \( w = 4, -\frac{2}{3} \) (Enter your response as: 4, -2/3)