To solve the equation [tex]\(3x^2 + 18x = 0\)[/tex], we can follow these steps:
1. Factor the equation: Start by factoring out the greatest common factor from each term.
[tex]\[
3x^2 + 18x = 0
\][/tex]
We can factor out [tex]\(3x\)[/tex] from both terms:
[tex]\[
3x(x + 6) = 0
\][/tex]
2. Apply the Zero Product Property: The Zero Product Property states that if a product of factors equals zero, at least one of the factors must be zero.
Thus, we set each factor equal to zero:
[tex]\[
3x = 0 \quad \text{or} \quad (x + 6) = 0
\][/tex]
3. Solve each equation: Solve for [tex]\(x\)[/tex] in each equation separately.
- For [tex]\(3x = 0\)[/tex]:
[tex]\[
\frac{3x}{3} = \frac{0}{3} \implies x = 0
\][/tex]
- For [tex]\(x + 6 = 0\)[/tex]:
[tex]\[
x + 6 - 6 = 0 - 6 \implies x = -6
\][/tex]
So, the solutions to the equation [tex]\(3x^2 + 18x = 0\)[/tex] are [tex]\(x = 0\)[/tex] and [tex]\(x = -6\)[/tex].
Thus, the values of [tex]\(x\)[/tex] are:
[tex]\[
x = -6 \quad \text{or} \quad x = 0
\][/tex]
