2y(y+4)=4

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


Simplifying
2y(y + 4) = 4

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

Solving
8y + 2y2 = 4

Solving for variable 'y'.

Reorder the terms:
-4 + 8y + 2y2 = 4 + -4

Combine like terms: 4 + -4 = 0
-4 + 8y + 2y2 = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 4y + y2)' equal to zero and attempt to solve:

Simplifying
-2 + 4y + y2 = 0

Solving
-2 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4y + 2 + y2 = 0 + 2

Reorder the terms:
-2 + 2 + 4y + y2 = 0 + 2

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

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

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = 2 + 4

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

Combine like terms: 2 + 4 = 6
4 + 4y + y2 = 6

Factor a perfect square on the left side:
(y + 2)(y + 2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(y + 2) equal to 2.449489743 and -2.449489743.


Subproblem 1
y + 2 = 2.449489743

Simplifying
y + 2 = 2.449489743

Reorder the terms:
2 + y = 2.449489743

Solving
2 + y = 2.449489743

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = 2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + y = 2.449489743 + -2
y = 2.449489743 + -2

Combine like terms: 2.449489743 + -2 = 0.449489743
y = 0.449489743

Simplifying
y = 0.449489743


Subproblem 2
y + 2 = -2.449489743

Simplifying
y + 2 = -2.449489743

Reorder the terms:
2 + y = -2.449489743

Solving
2 + y = -2.449489743

Solving for variable 'y'.

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

Add '-2' to each side of the equation.
2 + -2 + y = -2.449489743 + -2

Combine like terms: 2 + -2 = 0
0 + y = -2.449489743 + -2
y = -2.449489743 + -2

Combine like terms: -2.449489743 + -2 = -4.449489743
y = -4.449489743

Simplifying
y = -4.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.449489743, -4.449489743}
Solution
y = {0.449489743, -4.449489743}

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