Solve (15-5c)(5c + 5)(-c + 6) = 0
Understand the Problem
The question asks to solve an equation with a single variable 'c'. The equation is already factored, so the approach is to set each factor to zero and solve for 'c'. This will give the possible values of 'c' that satisfy the equation.
Answer
$c = 3, -1, 6$
Answer for screen readers
$c = 3, -1, 6$
Steps to Solve
- Set the first factor equal to zero
We have $15 - 5c = 0$.
- Solve for c
Add $5c$ to both sides: $15 = 5c$ Divide both sides by 5: $c = \frac{15}{5} = 3$
- Set the second factor equal to zero
We have $5c + 5 = 0$.
- Solve for c
Subtract 5 from both sides: $5c = -5$ Divide both sides by 5: $c = \frac{-5}{5} = -1$
- Set the third factor equal to zero
We have $-c + 6 = 0$.
- Solve for c
Add $c$ to both sides: $6 = c$ Thus, $c = 6$.
- List all solutions
The solutions are $c = 3$, $c = -1$, and $c = 6$.
$c = 3, -1, 6$
More Information
The problem leverages the zero-product property, which states that if the product of several factors is zero, then at least one of the factors must be zero.
Tips
A common mistake is not setting each factor to zero. Remember, each factor must be considered to find all possible solutions. Also, mistakes can occur while isolating $c$ in each equation, so care should be taken with the arithmetic.
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