2y(y+2)=y^2+12

Solution for 2y(y+2)=y^2+12 equation:

Simplifying
2y(y + 2) = y2 + 12

Reorder the terms:
2y(2 + y) = y2 + 12
(2 * 2y + y * 2y) = y2 + 12
(4y + 2y2) = y2 + 12

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

Solving
4y + 2y2 = 12 + y2

Solving for variable 'y'.

Reorder the terms:
-12 + 4y + 2y2 + -1y2 = 12 + y2 + -12 + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-12 + 4y + 1y2 = 12 + y2 + -12 + -1y2

Reorder the terms:
-12 + 4y + 1y2 = 12 + -12 + y2 + -1y2

Combine like terms: 12 + -12 = 0
-12 + 4y + 1y2 = 0 + y2 + -1y2
-12 + 4y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-12 + 4y + 1y2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
y = {-6, 2}