Use the zero product rule to solve the following equations for x x . 2 ( x − 4 ) ( x + 6 ) = 0 2\left(x-4\right)\left(x+6\right)=0

For this problem we've been asked to solve this equation for x using our zero product rule. Now remember the zero product rule simply says that any number multiplied by zero is going to equal zero. So if I plug a value in for x into our equation that turns our first factor here into zero, then the whole thing is going to equal zero. And same thing for our second factor. If I plug a value in for x that turns this factor into zero, then the whole thing is going to equal zero. So to solve this problem, we don't really need to do anything with this two here. In fact, we could divide it over to our other side and see that solving this equation for zero is the same thing as finding x minus four times x plus six equal to zero. So when does x minus four equal zero, or when does x plus six equal zero? For our first factor let's add four to both sides, and we get when x equals four as one of our solutions. And for our second factor let's subtract six from both sides and we get x equals negative six as our second solution. And we could always check our answers by taking our solutions and plugging them back into our original equation for x and making sure that the statement is true.

Use the zero product rule to solve the following equations for x x . 2 ( x − 4 ) ( x + 6 ) = 0 2\left(x-4\right)\left(x+6\right)=0

x = − 4 x=-4 or x = − 6 x=-6 x = − 6

7. Factoring

Quadratic Equations & Applications

Beginning Algebra

7. Factoring

Quadratic Equations & Applications

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Multiple Choice

Use the zero product rule to solve the following equations for $x$ .
$2 (x - 4) (x + 6) = 0$

$x equals 4$ or $x = - 6$

$x = - 4$ or $x equals 6$

$x=4$ or $x equals 6$

$x = - 4$ or $x=-6$

Verified step by step guidance

Start with the given equation: \$2\left(x-4\right)\left(x+6\right) = 0$.

Apply the zero product rule, which states that if a product of factors equals zero, then at least one of the factors must be zero. So, set each factor equal to zero separately: \$2 = 0$, $x - 4 = 0$, and $x + 6 = 0$.

Since \$2 = 0$ is never true, ignore this factor and focus on the other two equations: $x - 4 = 0$ and $x + 6 = 0$.

Solve each equation for $x$: For $x - 4 = 0$, add 4 to both sides to get $x = 4$. For $x + 6 = 0$, subtract 6 from both sides to get $x = -6$.

The solutions to the equation are the values of $x$ that make the original product zero, which are $x = 4$ and $x = -6$.

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Use the zero product rule to solve the following equations for $x$ .
$2 (x - 4) (x + 6) = 0$