(x%2B3)-(x-1)(x%2B4)%3D0.jpeg "(x+2)(x+3)-(x-1)(x+4)=0")
Solving the Equation (x+2)(x+3) - (x-1)(x+4) = 0
This article will guide you through the steps of solving the equation (x+2)(x+3) - (x-1)(x+4) = 0.
Expanding the Equation
First, we need to expand the equation by multiplying the factors:
- (x+2)(x+3): x² + 3x + 2x + 6 = x² + 5x + 6
- (x-1)(x+4): x² + 4x - x - 4 = x² + 3x - 4
Now, substitute these expanded expressions back into the original equation:
(x² + 5x + 6) - (x² + 3x - 4) = 0
Simplifying the Equation
Next, we simplify the equation by removing the parentheses and combining like terms:
x² + 5x + 6 - x² - 3x + 4 = 0 2x + 10 = 0
Isolating x
To solve for x, we need to isolate it on one side of the equation. Subtract 10 from both sides:
2x = -10
Solving for x
Finally, divide both sides by 2 to get the value of x:
x = -5
Conclusion
Therefore, the solution to the equation (x+2)(x+3) - (x-1)(x+4) = 0 is x = -5.