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

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


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

Reorder the terms:
(3 + 2y)(2y + 3) = 9

Reorder the terms:
(3 + 2y)(3 + 2y) = 9

Multiply (3 + 2y) * (3 + 2y)
(3(3 + 2y) + 2y * (3 + 2y)) = 9
((3 * 3 + 2y * 3) + 2y * (3 + 2y)) = 9
((9 + 6y) + 2y * (3 + 2y)) = 9
(9 + 6y + (3 * 2y + 2y * 2y)) = 9
(9 + 6y + (6y + 4y2)) = 9

Combine like terms: 6y + 6y = 12y
(9 + 12y + 4y2) = 9

Add '-9' to each side of the equation.
9 + 12y + -9 + 4y2 = 9 + -9

Reorder the terms:
9 + -9 + 12y + 4y2 = 9 + -9

Combine like terms: 9 + -9 = 0
0 + 12y + 4y2 = 9 + -9
12y + 4y2 = 9 + -9

Combine like terms: 9 + -9 = 0
12y + 4y2 = 0

Solving
12y + 4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(3 + y) = 0

Ignore the factor 4.

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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