2y(y+2)=72

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Solution for 2y(y+2)=72 equation: 


Simplifying
2y(y + 2) = 72

Reorder the terms:
2y(2 + y) = 72
(2 * 2y + y * 2y) = 72
(4y + 2y2) = 72

Solving
4y + 2y2 = 72

Solving for variable 'y'.

Reorder the terms:
-72 + 4y + 2y2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 4y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 2y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-36 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
-36 + 2y + y2 = 0

Solving
-36 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2y + 36 + y2 = 0 + 36

Reorder the terms:
-36 + 36 + 2y + y2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2y + y2 = 0 + 36
2y + y2 = 0 + 36

Combine like terms: 0 + 36 = 36
2y + y2 = 36

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 36 + 1

Reorder the terms:
1 + 2y + y2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + 2y + y2 = 37

Factor a perfect square on the left side:
(y + 1)(y + 1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(y + 1) equal to 6.08276253 and -6.08276253.


Subproblem 1
y + 1 = 6.08276253

Simplifying
y + 1 = 6.08276253

Reorder the terms:
1 + y = 6.08276253

Solving
1 + y = 6.08276253

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + y = 6.08276253 + -1
y = 6.08276253 + -1

Combine like terms: 6.08276253 + -1 = 5.08276253
y = 5.08276253

Simplifying
y = 5.08276253


Subproblem 2
y + 1 = -6.08276253

Simplifying
y + 1 = -6.08276253

Reorder the terms:
1 + y = -6.08276253

Solving
1 + y = -6.08276253

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + y = -6.08276253 + -1
y = -6.08276253 + -1

Combine like terms: -6.08276253 + -1 = -7.08276253
y = -7.08276253

Simplifying
y = -7.08276253


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.08276253, -7.08276253}
Solution
y = {5.08276253, -7.08276253}

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