y^2-10=4y+2

Solution for y^2-10=4y+2 equation:

Simplifying
y2 + -10 = 4y + 2

Reorder the terms:
-10 + y2 = 4y + 2

Reorder the terms:
-10 + y2 = 2 + 4y

Solving
-10 + y2 = 2 + 4y

Solving for variable 'y'.

Reorder the terms:
-10 + -2 + -4y + y2 = 2 + 4y + -2 + -4y

Combine like terms: -10 + -2 = -12
-12 + -4y + y2 = 2 + 4y + -2 + -4y

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

Combine like terms: 2 + -2 = 0
-12 + -4y + y2 = 0 + 4y + -4y
-12 + -4y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-12 + -4y + y2 = 0

Factor a trinomial.
(-2 + -1y)(6 + -1y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-2, 6}