y+10=y(y)-2

Solution for y+10=y(y)-2 equation:

Simplifying
y + 10 = y(y) + -2

Reorder the terms:
10 + y = y(y) + -2

Multiply y * y
10 + y = y2 + -2

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

Solving
10 + y = -2 + y2

Solving for variable 'y'.

Reorder the terms:
10 + 2 + y + -1y2 = -2 + y2 + 2 + -1y2

Combine like terms: 10 + 2 = 12
12 + y + -1y2 = -2 + y2 + 2 + -1y2

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

Combine like terms: -2 + 2 = 0
12 + y + -1y2 = 0 + y2 + -1y2
12 + y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
12 + y + -1y2 = 0

Factor a trinomial.
(4 + -1y)(3 + y) = 0

Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

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

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

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

Simplifying
y = -3
Solution
y = {4, -3}