2y^2+4y+6=(y+3)(y+3)

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Solution for 2y^2+4y+6=(y+3)(y+3) equation: 


Simplifying
2y2 + 4y + 6 = (y + 3)(y + 3)

Reorder the terms:
6 + 4y + 2y2 = (y + 3)(y + 3)

Reorder the terms:
6 + 4y + 2y2 = (3 + y)(y + 3)

Reorder the terms:
6 + 4y + 2y2 = (3 + y)(3 + y)

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

Combine like terms: 3y + 3y = 6y
6 + 4y + 2y2 = (9 + 6y + y2)

Solving
6 + 4y + 2y2 = 9 + 6y + y2

Solving for variable 'y'.

Reorder the terms:
6 + -9 + 4y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 6 + -9 = -3
-3 + 4y + -6y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 4y + -6y = -2y
-3 + -2y + 2y2 + -1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-3 + -2y + 1y2 = 9 + 6y + y2 + -9 + -6y + -1y2

Reorder the terms:
-3 + -2y + 1y2 = 9 + -9 + 6y + -6y + y2 + -1y2

Combine like terms: 9 + -9 = 0
-3 + -2y + 1y2 = 0 + 6y + -6y + y2 + -1y2
-3 + -2y + 1y2 = 6y + -6y + y2 + -1y2

Combine like terms: 6y + -6y = 0
-3 + -2y + 1y2 = 0 + y2 + -1y2
-3 + -2y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-3 + -2y + 1y2 = 0

Factor a trinomial.
(-1 + -1y)(3 + -1y) = 0


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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 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 + -1y = 0 + 1

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

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

Divide each side by '-1'.
y = -1

Simplifying
y = -1

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1, 3}

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