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Solve for [tex]c[/tex]:

[tex]
\begin{array}{l}
3c^2 = 27c \\
c = \square
\end{array}
[/tex]

(Simplify your answer. Use a comma to separate answers as needed.)

Answer :

To solve the equation [tex]\(3c^2 = 27c\)[/tex], we can follow these steps:

1. Set the Equation to Zero: Move all terms to one side of the equation to set it to zero.

[tex]\[
3c^2 - 27c = 0
\][/tex]

2. Factor the Equation: Notice that both terms have a common factor of [tex]\(3c\)[/tex]. Factor out [tex]\(3c\)[/tex]:

[tex]\[
3c(c - 9) = 0
\][/tex]

3. Apply the Zero Product Property: According to this property, if the product of two expressions is zero, then at least one of the expressions must be zero. So, set each factor equal to zero:

[tex]\[
3c = 0 \quad \text{or} \quad c - 9 = 0
\][/tex]

4. Solve Each Equation:

- For [tex]\(3c = 0\)[/tex], divide each side by 3:

[tex]\[
c = 0
\][/tex]

- For [tex]\(c - 9 = 0\)[/tex], add 9 to each side:

[tex]\[
c = 9
\][/tex]

Therefore, the solutions to the equation are [tex]\(c = 0\)[/tex] and [tex]\(c = 9\)[/tex].

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