Solving the Equation (x+3)(x7) = 0
This equation is a quadratic equation in factored form. We can use the Zero Product Property to solve for the values of x.
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.
Solving the Equation

Set each factor equal to zero:
 x + 3 = 0
 x  7 = 0

Solve each equation for x:
 x = 3
 x = 7
Therefore, the solutions to the equation (x+3)(x7) = 0 are x = 3 and x = 7.
Understanding the Solution
These solutions represent the points where the graph of the quadratic function y = (x+3)(x7) intersects the xaxis. These points are called the xintercepts.
In other words, the equation (x+3)(x7) = 0 represents the situation where the function y = (x+3)(x7) equals zero, which occurs at x = 3 and x = 7.