Question

Solve the equation.
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
xequals
  
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​(Use a comma to separate answers as needed. Type an integer or a simplified​ fraction.)

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:
\[
\frac{5}{2}, -4, 8.
\]