4y+(3+y)y=2

Solution for 4y+(3+y)y=2 equation:

Simplifying
4y + (3 + y) * y = 2

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

Combine like terms: 4y + 3y = 7y
7y + y2 = 2

Solving
7y + y2 = 2

Solving for variable 'y'.

Reorder the terms:
-2 + 7y + y2 = 2 + -2

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

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 7y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 7y + y2 = 0 + 2

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

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

The y term is 7y.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7y + 12.25 + y2 = 2 + 12.25

Reorder the terms:
12.25 + 7y + y2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + 7y + y2 = 14.25

Factor a perfect square on the left side:
(y + 3.5)(y + 3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(y + 3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
y + 3.5 = 3.774917218

Simplifying
y + 3.5 = 3.774917218

Reorder the terms:
3.5 + y = 3.774917218

Solving
3.5 + y = 3.774917218

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = 3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = 3.774917218 + -3.5
y = 3.774917218 + -3.5

Combine like terms: 3.774917218 + -3.5 = 0.274917218
y = 0.274917218

Simplifying
y = 0.274917218

Subproblem 2
y + 3.5 = -3.774917218

Simplifying
y + 3.5 = -3.774917218

Reorder the terms:
3.5 + y = -3.774917218

Solving
3.5 + y = -3.774917218

Solving for variable 'y'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + y = -3.774917218 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + y = -3.774917218 + -3.5
y = -3.774917218 + -3.5

Combine like terms: -3.774917218 + -3.5 = -7.274917218
y = -7.274917218

Simplifying
y = -7.274917218

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.274917218, -7.274917218}