Solve the equation.

Question

left parenthesis 2 x minus 5 right parenthesis left parenthesis x plus 4 right parenthesis left parenthesis x minus 8 right parenthesis equals 0
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Part 1
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Answer 1

To solve the equation

\[ (2x - 5)(x + 4)(x - 8) = 0, \]

we can set each factor equal to zero and solve for \( x \).

1. Set \( 2x - 5 = 0 \): \[ 2x = 5 \quad \Rightarrow \quad x = \frac{5}{2}. \]

2. Set \( x + 4 = 0 \): \[ x = -4. \]

3. Set \( x - 8 = 0 \): \[ x = 8. \]

Now we have the solutions: \[ x = \frac{5}{2}, -4, 8. \]

Thus, the final answer is: \[ \frac{5}{2}, -4, 8. \]