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(x-6)(x+5)=0

2 min read Jun 17, 2024
(x-6)(x+5)=0

Solving the Equation: (x-6)(x+5) = 0

This equation represents a simple quadratic equation in factored form. To solve it, we can use the Zero Product Property.

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.

In this case, we have two factors: (x-6) and (x+5). Therefore, for the product to be zero, at least one of these factors must equal zero.

Solving for x

Let's set each factor equal to zero and solve for x:

  • (x-6) = 0
    • Add 6 to both sides: x = 6
  • (x+5) = 0
    • Subtract 5 from both sides: x = -5

The Solutions

Therefore, the solutions to the equation (x-6)(x+5) = 0 are:

  • x = 6
  • x = -5

These solutions represent the points where the graph of the quadratic equation intersects the x-axis.

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