(2y+6)(2y+6)+y^2=36

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Solution for (2y+6)(2y+6)+y^2=36 equation: 


Simplifying
(2y + 6)(2y + 6) + y2 = 36

Reorder the terms:
(6 + 2y)(2y + 6) + y2 = 36

Reorder the terms:
(6 + 2y)(6 + 2y) + y2 = 36

Multiply (6 + 2y) * (6 + 2y)
(6(6 + 2y) + 2y * (6 + 2y)) + y2 = 36
((6 * 6 + 2y * 6) + 2y * (6 + 2y)) + y2 = 36
((36 + 12y) + 2y * (6 + 2y)) + y2 = 36
(36 + 12y + (6 * 2y + 2y * 2y)) + y2 = 36
(36 + 12y + (12y + 4y2)) + y2 = 36

Combine like terms: 12y + 12y = 24y
(36 + 24y + 4y2) + y2 = 36

Combine like terms: 4y2 + y2 = 5y2
36 + 24y + 5y2 = 36

Add '-36' to each side of the equation.
36 + 24y + -36 + 5y2 = 36 + -36

Reorder the terms:
36 + -36 + 24y + 5y2 = 36 + -36

Combine like terms: 36 + -36 = 0
0 + 24y + 5y2 = 36 + -36
24y + 5y2 = 36 + -36

Combine like terms: 36 + -36 = 0
24y + 5y2 = 0

Solving
24y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(24 + 5y) = 0


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

Subproblem 2
Set the factor '(24 + 5y)' equal to zero and attempt to solve:

Simplifying
24 + 5y = 0

Solving
24 + 5y = 0

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

Add '-24' to each side of the equation.
24 + -24 + 5y = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 5y = 0 + -24
5y = 0 + -24

Combine like terms: 0 + -24 = -24
5y = -24

Divide each side by '5'.
y = -4.8

Simplifying
y = -4.8
Solution
y = {0, -4.8}

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