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

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

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

Multiply (3 + -2y) * (3 + -2y)
(3(3 + -2y) + -2y * (3 + -2y)) + (3 + -2y) * y = 2
((3 * 3 + -2y * 3) + -2y * (3 + -2y)) + (3 + -2y) * y = 2
((9 + -6y) + -2y * (3 + -2y)) + (3 + -2y) * y = 2
(9 + -6y + (3 * -2y + -2y * -2y)) + (3 + -2y) * y = 2
(9 + -6y + (-6y + 4y2)) + (3 + -2y) * y = 2

Combine like terms: -6y + -6y = -12y
(9 + -12y + 4y2) + (3 + -2y) * y = 2

Reorder the terms for easier multiplication:
9 + -12y + 4y2 + y(3 + -2y) = 2
9 + -12y + 4y2 + (3 * y + -2y * y) = 2
9 + -12y + 4y2 + (3y + -2y2) = 2

Reorder the terms:
9 + -12y + 3y + 4y2 + -2y2 = 2

Combine like terms: -12y + 3y = -9y
9 + -9y + 4y2 + -2y2 = 2

Combine like terms: 4y2 + -2y2 = 2y2
9 + -9y + 2y2 = 2

Solving
9 + -9y + 2y2 = 2

Solving for variable 'y'.

Reorder the terms:
9 + -2 + -9y + 2y2 = 2 + -2

Combine like terms: 9 + -2 = 7
7 + -9y + 2y2 = 2 + -2

Combine like terms: 2 + -2 = 0
7 + -9y + 2y2 = 0

Factor a trinomial.
(1 + -1y)(7 + -2y) = 0

Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve:

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1y = 0 + -1
-1y = 0 + -1

Combine like terms: 0 + -1 = -1
-1y = -1

Divide each side by '-1'.
y = 1

Simplifying
y = 1
Subproblem 2
Set the factor '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {1, 3.5}