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Solving the Equation: (x+2)(x+3)=0
In this article, we will discuss how to solve the quadratic equation (x+2)(x+3)=0.
Expanding the Equation
To start, let's expand the equation by multiplying the two binomials:
(x+2)(x+3) = x^2 + 3x + 2x + 6 = x^2 + 5x + 6
So, our equation becomes:
x^2 + 5x + 6 = 0
Factoring the Quadratic
Now, let's try to factor the quadratic equation:
x^2 + 5x + 6 = (x + 2)(x + 3) = 0
Solving for x
To solve for x, we set each factor equal to 0 and solve for x:
x + 2 = 0 --> x = -2
x + 3 = 0 --> x = -3
Therefore, the solutions to the equation (x+2)(x+3)=0 are:
x = -2 and x = -3
Conclusion
In this article, we have successfully solved the quadratic equation (x+2)(x+3)=0 by expanding the equation, factoring the quadratic, and solving for x. The solutions to the equation are x = -2 and x = -3.
