Question

solve for z. separate multiple answers with a comma. (23z - 27)(30z - 23) = 0

Explanation:

Step1: Apply zero - product property

The zero - product property states that if \(ab = 0\), then either \(a=0\) or \(b = 0\). For the equation \((23z - 27)(30z - 23)=0\), we set each factor equal to zero:
\(23z-27 = 0\) or \(30z - 23=0\)

Step2: Solve \(23z-27 = 0\) for \(z\)

Add 27 to both sides of the equation \(23z-27 = 0\):
\(23z=27\)
Divide both sides by 23:
\(z=\frac{27}{23}\)

Step3: Solve \(30z - 23=0\) for \(z\)

Add 23 to both sides of the equation \(30z - 23=0\):
\(30z=23\)
Divide both sides by 30:
\(z=\frac{23}{30}\)

Answer:

\(\frac{27}{23},\frac{23}{30}\)