To solve the quadratic equation [tex]\( 12x^2 - 36x = 0 \)[/tex], we can follow these steps:
### Step 1: Factor the equation
First, observe that the equation can be factored by extracting the greatest common factor from both terms.
[tex]\[ 12x^2 - 36x = 0 \][/tex]
The greatest common factor here is [tex]\( 12x \)[/tex].
[tex]\[ 12x(x - 3) = 0 \][/tex]
### Step 2: Apply the Zero Product Property
Next, we can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Therefore, set each factor equal to zero:
[tex]\[ 12x = 0 \quad \text{or} \quad (x - 3) = 0 \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex]
Now, solve each equation separately:
1. For [tex]\( 12x = 0 \)[/tex]:
[tex]\[ x = 0 \][/tex]
2. For [tex]\( x - 3 = 0 \)[/tex]:
[tex]\[ x = 3 \][/tex]
### Conclusion
The solutions to the equation [tex]\( 12x^2 - 36x = 0 \)[/tex] are [tex]\( x = 0 \)[/tex] and [tex]\( x = 3 \)[/tex].
Therefore, the correct answer is:
A. [tex]\( x = 0, 3 \)[/tex]
