(y+3)(y+3)=2y^2+12y+14

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Solution for (y+3)(y+3)=2y^2+12y+14 equation: 


Simplifying
(y + 3)(y + 3) = 2y2 + 12y + 14

Reorder the terms:
(3 + y)(y + 3) = 2y2 + 12y + 14

Reorder the terms:
(3 + y)(3 + y) = 2y2 + 12y + 14

Multiply (3 + y) * (3 + y)
(3(3 + y) + y(3 + y)) = 2y2 + 12y + 14
((3 * 3 + y * 3) + y(3 + y)) = 2y2 + 12y + 14
((9 + 3y) + y(3 + y)) = 2y2 + 12y + 14
(9 + 3y + (3 * y + y * y)) = 2y2 + 12y + 14
(9 + 3y + (3y + y2)) = 2y2 + 12y + 14

Combine like terms: 3y + 3y = 6y
(9 + 6y + y2) = 2y2 + 12y + 14

Reorder the terms:
9 + 6y + y2 = 14 + 12y + 2y2

Solving
9 + 6y + y2 = 14 + 12y + 2y2

Solving for variable 'y'.

Reorder the terms:
9 + -14 + 6y + -12y + y2 + -2y2 = 14 + 12y + 2y2 + -14 + -12y + -2y2

Combine like terms: 9 + -14 = -5
-5 + 6y + -12y + y2 + -2y2 = 14 + 12y + 2y2 + -14 + -12y + -2y2

Combine like terms: 6y + -12y = -6y
-5 + -6y + y2 + -2y2 = 14 + 12y + 2y2 + -14 + -12y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-5 + -6y + -1y2 = 14 + 12y + 2y2 + -14 + -12y + -2y2

Reorder the terms:
-5 + -6y + -1y2 = 14 + -14 + 12y + -12y + 2y2 + -2y2

Combine like terms: 14 + -14 = 0
-5 + -6y + -1y2 = 0 + 12y + -12y + 2y2 + -2y2
-5 + -6y + -1y2 = 12y + -12y + 2y2 + -2y2

Combine like terms: 12y + -12y = 0
-5 + -6y + -1y2 = 0 + 2y2 + -2y2
-5 + -6y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-5 + -6y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 6y + y2) = 0

Factor a trinomial.
-1((5 + y)(1 + y)) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 0

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

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

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

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

Simplifying
y = -5

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

Simplifying
1 + y = 0

Solving
1 + y = 0

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 = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {-5, -1}

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