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(x-7)(x+3) 0

2 min read Jun 17, 2024
(x-7)(x+3) 0

Solving the Equation: (x-7)(x+3) = 0

This equation represents a quadratic expression set equal to zero. To solve for x, we can utilize the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying the Zero Product Property

  1. Set each factor equal to zero:

    • x - 7 = 0
    • x + 3 = 0

  2. Solve for x in each equation:

    • x = 7
    • x = -3

Solution

Therefore, the solutions to the equation (x-7)(x+3) = 0 are x = 7 and x = -3.

Verification

We can verify these solutions by plugging them back into the original equation:

  • For x = 7: (7-7)(7+3) = (0)(10) = 0
  • For x = -3: (-3-7)(-3+3) = (-10)(0) = 0

Since both solutions result in the equation being true, we have confirmed that x = 7 and x = -3 are the correct solutions.

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