(2x-3)(x+5)=0

2 min read Jun 16, 2024

Solving the Equation (2x-3)(x+5)=0

This equation is a quadratic equation in factored form. To find the solutions, we can use the Zero Product Property:

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation, we have two factors:

For the product of these factors to be zero, one or both of them must be equal to zero.

Step 1: Set each factor equal to zero:

Step 2: Solve each equation for x:

2x - 3 = 0
- Add 3 to both sides: 2x = 3
- Divide both sides by 2: x = 3/2
x + 5 = 0
- Subtract 5 from both sides: x = -5

Therefore, the solutions to the equation (2x-3)(x+5)=0 are x = 3/2 and x = -5.

This means that if we substitute either of these values for x in the original equation, the equation will be true.