(x%2B3)%2B(x-3)(x-2)-2x(x%2B1)%3D0.jpeg "(x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0")
Solving the Equation: (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0
This article will guide you through the steps to solve the given equation: (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0.
1. Expanding the Equation
First, we need to expand the equation by multiplying out the brackets:
- (x+2)(x+3) = x² + 5x + 6
- (x-3)(x-2) = x² - 5x + 6
- -2x(x+1) = -2x² - 2x
Now, substitute these expanded terms back into the original equation:
x² + 5x + 6 + x² - 5x + 6 - 2x² - 2x = 0
2. Simplifying the Equation
Combine like terms to simplify the equation:
(-2x² + x² + x²) + (5x - 5x - 2x) + (6 + 6) = 0
-2x + 12 = 0
3. Isolating the Variable
Next, isolate the variable term by subtracting 12 from both sides:
-2x = -12
4. Solving for x
Finally, divide both sides by -2 to solve for x:
x = 6
Conclusion
Therefore, the solution to the equation (x+2)(x+3)+(x-3)(x-2)-2x(x+1)=0 is x = 6.