(2y+1)(3y-2)-(6y-1)(y+4)=-20y

2 min read Jun 16, 2024
(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.

Related Post


Featured Posts