(y+6)(y+6)=2y^2+13y+6

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Solution for (y+6)(y+6)=2y^2+13y+6 equation: 


Simplifying
(y + 6)(y + 6) = 2y2 + 13y + 6

Reorder the terms:
(6 + y)(y + 6) = 2y2 + 13y + 6

Reorder the terms:
(6 + y)(6 + y) = 2y2 + 13y + 6

Multiply (6 + y) * (6 + y)
(6(6 + y) + y(6 + y)) = 2y2 + 13y + 6
((6 * 6 + y * 6) + y(6 + y)) = 2y2 + 13y + 6
((36 + 6y) + y(6 + y)) = 2y2 + 13y + 6
(36 + 6y + (6 * y + y * y)) = 2y2 + 13y + 6
(36 + 6y + (6y + y2)) = 2y2 + 13y + 6

Combine like terms: 6y + 6y = 12y
(36 + 12y + y2) = 2y2 + 13y + 6

Reorder the terms:
36 + 12y + y2 = 6 + 13y + 2y2

Solving
36 + 12y + y2 = 6 + 13y + 2y2

Solving for variable 'y'.

Reorder the terms:
36 + -6 + 12y + -13y + y2 + -2y2 = 6 + 13y + 2y2 + -6 + -13y + -2y2

Combine like terms: 36 + -6 = 30
30 + 12y + -13y + y2 + -2y2 = 6 + 13y + 2y2 + -6 + -13y + -2y2

Combine like terms: 12y + -13y = -1y
30 + -1y + y2 + -2y2 = 6 + 13y + 2y2 + -6 + -13y + -2y2

Combine like terms: y2 + -2y2 = -1y2
30 + -1y + -1y2 = 6 + 13y + 2y2 + -6 + -13y + -2y2

Reorder the terms:
30 + -1y + -1y2 = 6 + -6 + 13y + -13y + 2y2 + -2y2

Combine like terms: 6 + -6 = 0
30 + -1y + -1y2 = 0 + 13y + -13y + 2y2 + -2y2
30 + -1y + -1y2 = 13y + -13y + 2y2 + -2y2

Combine like terms: 13y + -13y = 0
30 + -1y + -1y2 = 0 + 2y2 + -2y2
30 + -1y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
30 + -1y + -1y2 = 0

Factor a trinomial.
(5 + -1y)(6 + y) = 0


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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {5, -6}

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