2y(y+1)=4

Solution for 2y(y+1)=4 equation:

Simplifying
2y(y + 1) = 4

Reorder the terms:
2y(1 + y) = 4
(1 * 2y + y * 2y) = 4
(2y + 2y2) = 4

Solving
2y + 2y2 = 4

Solving for variable 'y'.

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + y + y2) = 0

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

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-2, 1}