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(x-5)(x+2)(x+3)=0: Solving the Cubic Equation
In this article, we will be discussing the cubic equation (x-5)(x+2)(x+3)=0 and how to solve it. This equation is a product of three binomials, which makes it a bit more challenging to solve compared to a simple quadratic equation.
Factoring the Equation
To solve this equation, we can start by factoring it. Since the equation is already in factored form, we can see that it is a product of three binomials:
(x-5)(x+2)(x+3)=0
This tells us that either (x-5), (x+2), or (x+3) is equal to 0.
Solving for x
To find the solutions to the equation, we can set each of the binomials equal to 0 and solve for x.
(x-5)=0
x - 5 = 0 x = 5
(x+2)=0
x + 2 = 0 x = -2
(x+3)=0
x + 3 = 0 x = -3
Therefore, the solutions to the equation (x-5)(x+2)(x+3)=0 are x = 5, x = -2, and x = -3.
Conclusion
In conclusion, we have successfully solved the cubic equation (x-5)(x+2)(x+3)=0 by factoring and setting each of the binomials equal to 0. The solutions to the equation are x = 5, x = -2, and x = -3.
