(y*y*y)+(y*y)-2y+36=(y*y*y)+50

Solution for (y*y*y)+(y*y)-2y+36=(y*y*y)+50 equation:

Simplifying
(y * y * y) + (y * y) + -2y + 36 = (y * y * y) + 50

Multiply y * y
(y2 * y) + (y * y) + -2y + 36 = (y * y * y) + 50

Multiply y2 * y
(y3) + (y * y) + -2y + 36 = (y * y * y) + 50
y3 + (y * y) + -2y + 36 = (y * y * y) + 50

Multiply y * y
y3 + (y2) + -2y + 36 = (y * y * y) + 50
y3 + y2 + -2y + 36 = (y * y * y) + 50

Reorder the terms:
36 + -2y + y2 + y3 = (y * y * y) + 50

Multiply y * y
36 + -2y + y2 + y3 = (y2 * y) + 50

Multiply y2 * y
36 + -2y + y2 + y3 = (y3) + 50
36 + -2y + y2 + y3 = y3 + 50

Reorder the terms:
36 + -2y + y2 + y3 = 50 + y3

Add '-1y3' to each side of the equation.
36 + -2y + y2 + y3 + -1y3 = 50 + y3 + -1y3

Combine like terms: y3 + -1y3 = 0
36 + -2y + y2 + 0 = 50 + y3 + -1y3
36 + -2y + y2 = 50 + y3 + -1y3

Combine like terms: y3 + -1y3 = 0
36 + -2y + y2 = 50 + 0
36 + -2y + y2 = 50

Solving
36 + -2y + y2 = 50

Solving for variable 'y'.

Reorder the terms:
36 + -50 + -2y + y2 = 50 + -50

Combine like terms: 36 + -50 = -14
-14 + -2y + y2 = 50 + -50

Combine like terms: 50 + -50 = 0
-14 + -2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -2y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -2y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -2y + y2 = 0 + 14
-2y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-2y + y2 = 14

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 14 + 1

Reorder the terms:
1 + -2y + y2 = 14 + 1

Combine like terms: 14 + 1 = 15
1 + -2y + y2 = 15

Factor a perfect square on the left side:
(y + -1)(y + -1) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(y + -1) equal to 3.872983346 and -3.872983346.

Subproblem 1
y + -1 = 3.872983346

Simplifying
y + -1 = 3.872983346

Reorder the terms:
-1 + y = 3.872983346

Solving
-1 + y = 3.872983346

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = 3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3.872983346 + 1
y = 3.872983346 + 1

Combine like terms: 3.872983346 + 1 = 4.872983346
y = 4.872983346

Simplifying
y = 4.872983346

Subproblem 2
y + -1 = -3.872983346

Simplifying
y + -1 = -3.872983346

Reorder the terms:
-1 + y = -3.872983346

Solving
-1 + y = -3.872983346

Solving for variable 'y'.

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

Add '1' to each side of the equation.
-1 + 1 + y = -3.872983346 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3.872983346 + 1
y = -3.872983346 + 1

Combine like terms: -3.872983346 + 1 = -2.872983346
y = -2.872983346

Simplifying
y = -2.872983346

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.872983346, -2.872983346}