(x-1)-(x%2B2)(2x%2B1)%3D0.jpeg "(2x+2)(x-1)-(x+2)(2x+1)=0")
Solving the Equation: (2x+2)(x-1)-(x+2)(2x+1)=0
This article will walk you through the process of solving the algebraic equation: (2x+2)(x-1)-(x+2)(2x+1)=0.
Expanding the Equation
First, we need to expand the equation by multiplying the terms in each set of parentheses.
- (2x+2)(x-1):
- 2x * x = 2x²
- 2x * -1 = -2x
- 2 * x = 2x
- 2 * -1 = -2
- (x+2)(2x+1):
- x * 2x = 2x²
- x * 1 = x
- 2 * 2x = 4x
- 2 * 1 = 2
Putting these together, our equation becomes:
2x² - 2x + 2x - 2 - (2x² + x + 4x + 2) = 0
Simplifying the Equation
Next, we can simplify the equation by combining like terms:
- 2x² - 2x² = 0
- -2x + 2x = 0
- x + 4x = 5x
- -2 - 2 = -4
Our simplified equation is now:
-5x - 4 = 0
Solving for x
Finally, we can solve for x:
- Add 4 to both sides: -5x = 4
- Divide both sides by -5: x = -4/5
Therefore, the solution to the equation (2x+2)(x-1)-(x+2)(2x+1)=0 is x = -4/5.