(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 quadratic equation in factored form. To solve for the values of x that satisfy this equation, we can utilize 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.

Applying the Zero Product Property

In our equation, we have two factors:

• (x+6)
• (-x+1)

According to the Zero Product Property, either (x+6) = 0 or (-x+1) = 0.

Solving for x

1. For (x+6) = 0:

   • Subtract 6 from both sides:
     • x = -6

2. For (-x+1) = 0:

   • Subtract 1 from both sides:
     • -x = -1
   • Multiply both sides by -1:
     • x = 1

Solutions

Therefore, the solutions to the equation (x+6)(-x+1) = 0 are x = -6 and x = 1.

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