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Solving the Equation: 0 = 2x(x-5) + 8(x-5)
This article will guide you through the steps of solving the given equation: 0 = 2x(x-5) + 8(x-5)
1. Factoring out the Common Factor
The equation has a common factor of (x-5). We can factor it out as follows:
0 = (x-5) (2x + 8)
2. Setting each factor to zero
To find the solutions, we need to set each factor equal to zero and solve for x:
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x - 5 = 0 Adding 5 to both sides gives us: x = 5
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2x + 8 = 0 Subtracting 8 from both sides gives us: 2x = -8 Dividing both sides by 2 gives us: x = -4
3. The Solutions
Therefore, the solutions to the equation 0 = 2x(x-5) + 8(x-5) are x = 5 and x = -4.
Conclusion
We have successfully solved the given equation by factoring and setting each factor to zero. This method provides a straightforward approach to finding the solutions.