(x%2B6)%3D0.jpeg "(2x-10)(x+6)=0")
Solving the Equation: (2x-10)(x+6) = 0
This equation is a quadratic equation in factored form. To solve for x, we can use the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.
Let's apply this to our equation:
- (2x-10)(x+6) = 0
This means either:
- 2x-10 = 0 or
- x+6 = 0
Now, we can solve each of these linear equations for x:
1. 2x-10 = 0
- Add 10 to both sides: 2x = 10
- Divide both sides by 2: x = 5
2. x+6 = 0
- Subtract 6 from both sides: x = -6
Therefore, the solutions to the equation (2x-10)(x+6) = 0 are x = 5 and x = -6.
These are the values of x that make the entire equation true, as they result in one or both of the factors equaling zero.