Question

solve for x .
\\((x^2 - 7x + 6)(6x + 6) = 0\\)
(if there is more than one solution, separate them with commas.)
\\(x = \square\\)

Explanation:

Step1: Apply Zero-Product Property

If \( (a)(b) = 0 \), then \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero:

1. \( x^2 - 7x + 6 = 0 \)
2. \( 6x + 6 = 0 \)

Step2: Solve \( x^2 - 7x + 6 = 0 \)

Factor the quadratic: \( (x - 1)(x - 6) = 0 \).
Set each factor to zero:

• \( x - 1 = 0 \Rightarrow x = 1 \)
• \( x - 6 = 0 \Rightarrow x = 6 \)

Step3: Solve \( 6x + 6 = 0 \)

Subtract 6: \( 6x = -6 \).
Divide by 6: \( x = -1 \)

Answer:

\( x = 1, 6, -1 \)