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Solving the Equation (x+2)(x+3)=12
This equation involves a quadratic expression, meaning we need to solve for the values of x that satisfy the equation. Here's how to solve it:
Step 1: Expand the Equation
First, expand the left side of the equation using the distributive property (FOIL method):
(x+2)(x+3) = x² + 3x + 2x + 6
This simplifies to:
x² + 5x + 6 = 12
Step 2: Set the Equation to Zero
To solve for x, we need to have the equation in standard quadratic form (ax² + bx + c = 0). So, subtract 12 from both sides:
x² + 5x + 6 - 12 = 0
This gives us:
x² + 5x - 6 = 0
Step 3: Factor the Quadratic Equation
Now, we factor the quadratic equation:
(x+6)(x-1) = 0
Step 4: Solve for x
For the product of two factors to be zero, at least one of them must be zero. So, we have two possible solutions:
- x + 6 = 0 => x = -6
- x - 1 = 0 => x = 1
Conclusion
Therefore, the solutions to the equation (x+2)(x+3) = 12 are x = -6 and x = 1.