(x%2B3)%3D(x-5)(x%2B1).jpeg "(x-2)(x+3)=(x-5)(x+1)")
Solving the Equation (x-2)(x+3) = (x-5)(x+1)
This equation represents a quadratic equation, and we can solve it by expanding both sides and rearranging terms.
Step 1: Expand both sides of the equation.
Using the FOIL method (First, Outer, Inner, Last), we can expand both sides:
- Left Side: (x-2)(x+3) = x² + x - 6
- Right Side: (x-5)(x+1) = x² - 4x - 5
Step 2: Simplify the equation.
Now our equation becomes:
x² + x - 6 = x² - 4x - 5
Step 3: Combine like terms.
To simplify further, we can subtract x² from both sides, leaving:
x - 6 = -4x - 5
Step 4: Isolate the variable x.
Add 4x to both sides:
5x - 6 = -5
Step 5: Solve for x.
Add 6 to both sides:
5x = 1
Finally, divide both sides by 5:
x = 1/5
Therefore, the solution to the equation (x-2)(x+3) = (x-5)(x+1) is x = 1/5.