Question $(5 x+10)(18 x+6)=0$

Studdy Solution

STEP 1

What is this asking? We're looking for the values of $x$ that make this whole equation equal to zero! Watch out! Remember, if either of the factors equals zero, the whole thing becomes zero.
Don't forget to solve for both factors!

STEP 2

1. Set the first factor to zero and solve.
2. Set the second factor to zero and solve.

STEP 3

Let's take that first part, $5x + 10$ , and set it equal to zero: $5x + 10 = 0$

STEP 4

To get $x$ by itself, let's subtract $\bf{10}$ from both sides: $5x + 10 - 10 = 0 - 10$ $5x = -10$

STEP 5

Now, let's divide both sides by $\bf{5}$ to isolate $x$ : $\frac{5x}{5} = \frac{-10}{5}$ $x = -2$ So, one possible value for $x$ is $\bf{-2}$ !

STEP 6

Now, let's work with the second part, $18x + 6$ , and set it equal to zero: $18x + 6 = 0$

STEP 7

Let's subtract $\bf{6}$ from both sides: $18x + 6 - 6 = 0 - 6$ $18x = -6$

STEP 8

Finally, divide both sides by $\bf{18}$ to get $x$ all alone: $\frac{18x}{18} = \frac{-6}{18}$ $x = -\frac{6}{18}$ $x = -\frac{1}{3}$ So, our second possible value for $x$ is $\bf{-\frac{1}{3}}$ !

STEP 9

We found two values for $x$ that make the original equation true: $x = \bf{-2}$ and $x = \bf{-\frac{1}{3}}$ .
Awesome!

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