Question

solve for all values of ( x ) by factoring.

( x^2 - 6x = 0 )

Explanation:

Step1: Factor out the common term

We can factor out an \( x \) from the left - hand side of the equation \( x^{2}-6x = 0 \). Using the distributive property in reverse (\( ab+ac=a(b + c) \), here \( a=x \), \( b=x \), \( c=- 6 \)), we get \( x(x - 6)=0 \).

Step2: Apply the zero - product property

The zero - product property states that if \( ab = 0 \), then either \( a=0 \) or \( b = 0 \) (or both). So, for the equation \( x(x - 6)=0 \), we set each factor equal to zero:

• Case 1: \( x=0 \)
• Case 2: \( x - 6=0 \), and solving for \( x \) gives \( x=6 \)

Answer:

The solutions are \( x = 0 \) and \( x=6 \)