Solving the Equation (x+2)^2*(x7)*(x+5) = 0
This equation is a polynomial equation and we can solve it by finding the values of x that make the equation true.
Understanding the Equation
 The equation is set to zero. This means we are looking for the points where the expression on the lefthand side equals zero.
 The expression is a product of four factors: (x+2)^2, (x7), and (x+5).
The Zero Product Property
The key to solving this equation is the Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.
Solving for x
To find the solutions, we set each factor equal to zero and solve for x:

(x+2)^2 = 0
 Take the square root of both sides: x + 2 = 0
 Solve for x: x = 2

(x7) = 0
 Solve for x: x = 7

(x+5) = 0
 Solve for x: x = 5
The Solutions
Therefore, the solutions to the equation (x+2)^2*(x7)*(x+5) = 0 are:
 x = 2 (This solution has a multiplicity of 2 because the factor (x+2) appears squared.)
 x = 7
 x = 5
Conclusion
The equation (x+2)^2*(x7)*(x+5) = 0 has three solutions: x = 2, x = 7, and x = 5. These are the values of x that make the expression on the lefthand side equal to zero.