(x%2B3)-(x-2)(x-5)%3D-4.jpeg "(x+2)(x+3)-(x-2)(x-5)=-4")
Solving the Equation: (x+2)(x+3)-(x-2)(x-5)=-4
This article will walk you through the process of solving the equation (x+2)(x+3)-(x-2)(x-5)=-4.
Expanding the Equation
First, we need to expand the equation by multiplying out the brackets:
- (x+2)(x+3): This expands to x² + 5x + 6 using the FOIL method (First, Outer, Inner, Last).
- (x-2)(x-5): This expands to x² - 7x + 10 using the FOIL method.
Now, our equation becomes: x² + 5x + 6 - (x² - 7x + 10) = -4
Simplifying the Equation
Next, we can simplify the equation by distributing the negative sign:
x² + 5x + 6 - x² + 7x - 10 = -4
Combining like terms, we get: 12x - 4 = -4
Isolating the Variable
Now, let's isolate the variable x by adding 4 to both sides:
12x = 0
Solving for x
Finally, divide both sides by 12 to solve for x:
x = 0
Conclusion
Therefore, the solution to the equation (x+2)(x+3)-(x-2)(x-5)=-4 is x = 0.