(x-6)(x+1)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x - 6)(x + 1) = 0

This equation represents a simple quadratic equation in factored form. To solve for the values of 'x' that satisfy the equation, 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 equal to zero, then at least one of the factors must be equal to zero.

Applying the Property

In our equation, (x - 6)(x + 1) = 0, we have two factors: (x - 6) and (x + 1). Applying the Zero Product Property, we set each factor equal to zero and solve for 'x':

• x - 6 = 0 Adding 6 to both sides, we get: x = 6

• x + 1 = 0 Subtracting 1 from both sides, we get: x = -1

Solution

Therefore, the solutions to the equation (x - 6)(x + 1) = 0 are x = 6 and x = -1. These values are the roots of the quadratic equation, which represent the points where the graph of the equation intersects the x-axis.