(2y-3)*(y+1)+y*(y-2)=3*(y+2)2

Solution for (2y-3)*(y+1)+y*(y-2)=3*(y+2)2 equation:

Simplifying
(2y + -3)(y + 1) + y(y + -2) = 3(y + 2) * 2

Reorder the terms:
(-3 + 2y)(y + 1) + y(y + -2) = 3(y + 2) * 2

Reorder the terms:
(-3 + 2y)(1 + y) + y(y + -2) = 3(y + 2) * 2

Multiply (-3 + 2y) * (1 + y)
(-3(1 + y) + 2y * (1 + y)) + y(y + -2) = 3(y + 2) * 2
((1 * -3 + y * -3) + 2y * (1 + y)) + y(y + -2) = 3(y + 2) * 2
((-3 + -3y) + 2y * (1 + y)) + y(y + -2) = 3(y + 2) * 2
(-3 + -3y + (1 * 2y + y * 2y)) + y(y + -2) = 3(y + 2) * 2
(-3 + -3y + (2y + 2y2)) + y(y + -2) = 3(y + 2) * 2

Combine like terms: -3y + 2y = -1y
(-3 + -1y + 2y2) + y(y + -2) = 3(y + 2) * 2

Reorder the terms:
-3 + -1y + 2y2 + y(-2 + y) = 3(y + 2) * 2
-3 + -1y + 2y2 + (-2 * y + y * y) = 3(y + 2) * 2
-3 + -1y + 2y2 + (-2y + y2) = 3(y + 2) * 2

Reorder the terms:
-3 + -1y + -2y + 2y2 + y2 = 3(y + 2) * 2

Combine like terms: -1y + -2y = -3y
-3 + -3y + 2y2 + y2 = 3(y + 2) * 2

Combine like terms: 2y2 + y2 = 3y2
-3 + -3y + 3y2 = 3(y + 2) * 2

Reorder the terms:
-3 + -3y + 3y2 = 3(2 + y) * 2

Reorder the terms for easier multiplication:
-3 + -3y + 3y2 = 3 * 2(2 + y)

Multiply 3 * 2
-3 + -3y + 3y2 = 6(2 + y)
-3 + -3y + 3y2 = (2 * 6 + y * 6)
-3 + -3y + 3y2 = (12 + 6y)

Solving
-3 + -3y + 3y2 = 12 + 6y

Solving for variable 'y'.

Reorder the terms:
-3 + -12 + -3y + -6y + 3y2 = 12 + 6y + -12 + -6y

Combine like terms: -3 + -12 = -15
-15 + -3y + -6y + 3y2 = 12 + 6y + -12 + -6y

Combine like terms: -3y + -6y = -9y
-15 + -9y + 3y2 = 12 + 6y + -12 + -6y

Reorder the terms:
-15 + -9y + 3y2 = 12 + -12 + 6y + -6y

Combine like terms: 12 + -12 = 0
-15 + -9y + 3y2 = 0 + 6y + -6y
-15 + -9y + 3y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-15 + -9y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -3y + y2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -3y + y2)' equal to zero and attempt to solve:

Simplifying
-5 + -3y + y2 = 0

Solving
-5 + -3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -3y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + -3y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3y + y2 = 0 + 5
-3y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
-3y + y2 = 5

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = 5 + 2.25

Reorder the terms:
2.25 + -3y + y2 = 5 + 2.25

Combine like terms: 5 + 2.25 = 7.25
2.25 + -3y + y2 = 7.25

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + -1.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
y + -1.5 = 2.692582404

Simplifying
y + -1.5 = 2.692582404

Reorder the terms:
-1.5 + y = 2.692582404

Solving
-1.5 + y = 2.692582404

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = 2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = 2.692582404 + 1.5
y = 2.692582404 + 1.5

Combine like terms: 2.692582404 + 1.5 = 4.192582404
y = 4.192582404

Simplifying
y = 4.192582404

Subproblem 2
y + -1.5 = -2.692582404

Simplifying
y + -1.5 = -2.692582404

Reorder the terms:
-1.5 + y = -2.692582404

Solving
-1.5 + y = -2.692582404

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1.5' to each side of the equation.
-1.5 + 1.5 + y = -2.692582404 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + y = -2.692582404 + 1.5
y = -2.692582404 + 1.5

Combine like terms: -2.692582404 + 1.5 = -1.192582404
y = -1.192582404

Simplifying
y = -1.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.192582404, -1.192582404}
Solution
y = {4.192582404, -1.192582404}