(x%2B5)%2B12%3D(x%2B3)(x-4)-2.jpeg "(x-2)(x+5)+12=(x+3)(x-4)-2")
Solving the Equation: (x-2)(x+5)+12=(x+3)(x-4)-2
This article will guide you through solving the equation (x-2)(x+5)+12=(x+3)(x-4)-2. We will use algebraic manipulation to find the solution for x.
Expanding the Equation
First, we need to expand both sides of the equation by multiplying the terms within the parentheses.
- Left Side: (x-2)(x+5) + 12 = x² + 3x - 10 + 12 = x² + 3x + 2
- Right Side: (x+3)(x-4) - 2 = x² - x - 12 - 2 = x² - x - 14
Now, the equation becomes: x² + 3x + 2 = x² - x - 14
Isolating x
To solve for x, we need to isolate the variable on one side of the equation. We can do this by subtracting x² from both sides:
3x + 2 = -x - 14
Next, add x to both sides:
4x + 2 = -14
Finally, subtract 2 from both sides:
4x = -16
Solving for x
Now, we can solve for x by dividing both sides by 4:
x = -4
Therefore, the solution to the equation (x-2)(x+5)+12=(x+3)(x-4)-2 is x = -4.
You can verify this solution by plugging it back into the original equation and confirming that both sides are equal.