4y(2y+1)=4

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

Simplifying
4y(2y + 1) = 4

Reorder the terms:
4y(1 + 2y) = 4
(1 * 4y + 2y * 4y) = 4
(4y + 8y2) = 4

Solving
4y + 8y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 4y + 8y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 4y + 8y2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + y + 2y2) = 0

Factor a trinomial.
4((-1 + -1y)(1 + -2y)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -2y)' equal to zero and attempt to solve:

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {-1, 0.5}