((y+3)(y+3))+y^2=9

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Solution for ((y+3)(y+3))+y^2=9 equation: 


Simplifying
((y + 3)(y + 3)) + y2 = 9

Reorder the terms:
((3 + y)(y + 3)) + y2 = 9

Reorder the terms:
((3 + y)(3 + y)) + y2 = 9

Multiply (3 + y) * (3 + y)
((3(3 + y) + y(3 + y))) + y2 = 9
(((3 * 3 + y * 3) + y(3 + y))) + y2 = 9
(((9 + 3y) + y(3 + y))) + y2 = 9
((9 + 3y + (3 * y + y * y))) + y2 = 9
((9 + 3y + (3y + y2))) + y2 = 9

Combine like terms: 3y + 3y = 6y
((9 + 6y + y2)) + y2 = 9
(9 + 6y + y2) + y2 = 9

Remove parenthesis around (9 + 6y + y2)
9 + 6y + y2 + y2 = 9

Combine like terms: y2 + y2 = 2y2
9 + 6y + 2y2 = 9

Add '-9' to each side of the equation.
9 + 6y + -9 + 2y2 = 9 + -9

Reorder the terms:
9 + -9 + 6y + 2y2 = 9 + -9

Combine like terms: 9 + -9 = 0
0 + 6y + 2y2 = 9 + -9
6y + 2y2 = 9 + -9

Combine like terms: 9 + -9 = 0
6y + 2y2 = 0

Solving
6y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2y'.
2y(3 + y) = 0

Ignore the factor 2.

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 '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {0, -3}

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