Solve w(w-6)(w-6) = 0
Understand the Problem
The question is straightforward, it asks us to solve the equation w(w-6)(w-6) = 0 for the variable 'w'. This involves finding the values of 'w' that make the equation true. We can do this by setting each factor equal to zero and solving for 'w'.
Answer
$w = 0, 6$
Answer for screen readers
$w = 0, 6$
Steps to Solve
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Set the first factor equal to zero We have the factor $w$, so we set it equal to zero: $w = 0$
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Set the second factor equal to zero We have the factor $(w - 6)$, so we set it equal to zero: $w - 6 = 0$
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Solve for $w$ Add 6 to both sides of the equation: $w = 6$
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Set the third factor equal to zero We have the factor $(w - 6)$ again, so we set it equal to zero: $w - 6 = 0$
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Solve for $w$ Add 6 to both sides of the equation: $w = 6$
$w = 0, 6$
More Information
The equation $w(w-6)(w-6) = 0$ has two distinct solutions: $w = 0$ and $w = 6$. The solution $w = 6$ has a multiplicity of 2 because the factor $(w-6)$ appears twice.
Tips
A common mistake is only identifying one of the solutions, particularly overlooking $w=0$. Another mistake is thinking there should be three different answers since there are three factors, not recognizing that $(w-6)$ is repeated.
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