0 2x(x-5)+8(x-5)=0

2 min read Jun 17, 2024
0 2x(x-5)+8(x-5)=0

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:

  • x - 5 = 0 Adding 5 to both sides gives us: x = 5

  • 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.

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