Question

Solve.left parenthesis x minus 5 right parenthesis left parenthesis 4 x plus 9 right parenthesis equals 0Question content area bottomPart 1The solution is xequalsenter your response here.​(Use a comma to separate answers as​ needed.)

Answer 1

To solve the equation \((x - 5)(4x + 9) = 0\), we can use the zero product property, which states that if a product of two factors equals zero, then at least one of the factors must be zero.

We set each factor equal to zero:

1. \(x - 5 = 0\)
2. \(4x + 9 = 0\)

Now, let's solve each equation:

1. For \(x - 5 = 0\):
\[
x = 5
\]

2. For \(4x + 9 = 0\):
\[
4x = -9 \implies x = -\frac{9}{4}
\]

So, the solutions are:
\[
x = 5, -\frac{9}{4}
\]

Thus, the final answer is:
\[
x = 5, -\frac{9}{4}
\]