To solve the equation [tex]\( 6x^2 = 18x \)[/tex] for [tex]\( x \)[/tex], let's follow a step-by-step process:
1. Rewrite the equation: Start by bringing all terms to one side of the equation to set it to zero.
[tex]\[
6x^2 - 18x = 0
\][/tex]
2. Factor the equation: Factor out the greatest common factor (GCF), which in this case is [tex]\( 6x \)[/tex].
[tex]\[
6x(x - 3) = 0
\][/tex]
3. Set each factor to zero: In this factored form, the equation will be zero if either factor is zero. So, set each factor equal to zero:
[tex]\[
6x = 0 \quad \text{or} \quad x - 3 = 0
\][/tex]
4. Solve each equation:
- For [tex]\( 6x = 0 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
x = 0
\][/tex]
- For [tex]\( x - 3 = 0 \)[/tex], solve for [tex]\( x \)[/tex]:
[tex]\[
x = 3
\][/tex]
5. List the solutions: The solutions to the equation are [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex].
Therefore, the solutions are:
[tex]\[
x = 0, 3
\][/tex]
