(3y-2)-(6y-1)(y%2B4)%3D-20y.jpeg "(2y+1)(3y-2)-(6y-1)(y+4)=-20y")
Solving the Equation: (2y+1)(3y-2)-(6y-1)(y+4)=-20y
This article will guide you through the steps of solving the given equation: (2y+1)(3y-2)-(6y-1)(y+4)=-20y. We will use algebraic manipulation to simplify the equation and arrive at the solution for y.
Expanding the Equation
First, we need to expand the equation by multiplying the terms within the brackets:
- (2y+1)(3y-2) = 6y² - 4y + 3y - 2 = 6y² - y - 2
- (6y-1)(y+4) = 6y² + 24y - y - 4 = 6y² + 23y - 4
Now, our equation looks like this: 6y² - y - 2 - (6y² + 23y - 4) = -20y
Simplifying the Equation
Next, we distribute the negative sign:
6y² - y - 2 - 6y² - 23y + 4 = -20y
Combine like terms:
-24y + 2 = -20y
Isolating y
To isolate y, move all the y terms to one side of the equation and the constant term to the other side:
-24y + 20y = -2
-4y = -2
Solving for y
Finally, divide both sides of the equation by -4 to solve for y:
y = (-2) / (-4)
y = 1/2
Therefore, the solution to the equation (2y+1)(3y-2)-(6y-1)(y+4)=-20y is y = 1/2.