2y+3+y^2-5+y=33

Solution for 2y+3+y^2-5+y=33 equation:

Simplifying
2y + 3 + y2 + -5 + y = 33

Reorder the terms:
3 + -5 + 2y + y + y2 = 33

Combine like terms: 3 + -5 = -2
-2 + 2y + y + y2 = 33

Combine like terms: 2y + y = 3y
-2 + 3y + y2 = 33

Solving
-2 + 3y + y2 = 33

Solving for variable 'y'.

Reorder the terms:
-2 + -33 + 3y + y2 = 33 + -33

Combine like terms: -2 + -33 = -35
-35 + 3y + y2 = 33 + -33

Combine like terms: 33 + -33 = 0
-35 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 3y + 35 + y2 = 0 + 35

Reorder the terms:
-35 + 35 + 3y + y2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 3y + y2 = 0 + 35
3y + y2 = 0 + 35

Combine like terms: 0 + 35 = 35
3y + y2 = 35

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 = 35 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 35 + 2.25

Combine like terms: 35 + 2.25 = 37.25
2.25 + 3y + y2 = 37.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(y + 1.5) equal to 6.103277808 and -6.103277808.

Subproblem 1
y + 1.5 = 6.103277808

Simplifying
y + 1.5 = 6.103277808

Reorder the terms:
1.5 + y = 6.103277808

Solving
1.5 + y = 6.103277808

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 = 6.103277808 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 6.103277808 + -1.5
y = 6.103277808 + -1.5

Combine like terms: 6.103277808 + -1.5 = 4.603277808
y = 4.603277808

Simplifying
y = 4.603277808

Subproblem 2
y + 1.5 = -6.103277808

Simplifying
y + 1.5 = -6.103277808

Reorder the terms:
1.5 + y = -6.103277808

Solving
1.5 + y = -6.103277808

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 = -6.103277808 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -6.103277808 + -1.5
y = -6.103277808 + -1.5

Combine like terms: -6.103277808 + -1.5 = -7.603277808
y = -7.603277808

Simplifying
y = -7.603277808

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.603277808, -7.603277808}