Gross Schofield
09/14/2023 · Senior High School
Solving an equation written in factored form Solve. \( \quad-5(u-2)(-u+9)=0 \)
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Step-by-step Solution
To solve the equation \(-5(u-2)(-u+9)=0\), we can start by setting the factored expression equal to zero. Since the product of the factors equals zero, at least one of the factors must be zero.
First, we can simplify the equation by dividing both sides by \(-5\) (since \(-5\) is not zero, this does not change the equality):
\[
(u-2)(-u+9) = 0
\]
Next, we set each factor equal to zero:
1. \(u - 2 = 0\)
2. \(-u + 9 = 0\)
Now, we solve each equation:
1. For \(u - 2 = 0\):
\[
u = 2
\]
2. For \(-u + 9 = 0\):
\[
-u = -9 \quad \Rightarrow \quad u = 9
\]
Thus, the solutions to the equation \(-5(u-2)(-u+9)=0\) are:
\[
\boxed{2} \quad \text{and} \quad \boxed{9}
\]
Quick Answer
The solutions are \( u = 2 \) and \( u = 9 \).
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