Question

solve for all values of x by factoring.

x² - 6x = 0

answer attempt 1 out of 2

Explanation:

Step1: Factor out common term

The equation is \(x^{2}-6x = 0\). We can factor out an \(x\) from both terms on the left - hand side. 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 zero - product property

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

• Case 1: \(x=0\)
• Case 2: \(x - 6=0\). Solving for \(x\) in this equation, we add 6 to both sides, so \(x=6\).

Answer:

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