Question

Find the values of x that make the following equation equal zero: $(x+4)(x-2)=0$
$x=-4$ and $x=2$
$x=-2$ and $x=4$
$x=2$ and $x=4$
$x=-2$ and $x=-4$

Answer 1

To solve the equation \((x+4)(x-2)=0\), we can use the property that if a product of two factors is zero, at least one of the factors must be zero. We can set each factor equal to zero and solve for \(x\).

1. Set the first factor equal to zero:
\[
x + 4 = 0
\]
Subtracting 4 from both sides gives:
\[
x = -4
\]

2. Set the second factor equal to zero:
\[
x - 2 = 0
\]
Adding 2 to both sides gives:
\[
x = 2
\]

Now we have found two solutions:

\[
x = -4 \quad \text{and} \quad x = 2
\]

Therefore, the values of \(x\) that make the equation equal to zero are:

\[
\boxed{-4 \text{ and } 2}
\]