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

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


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

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

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

Multiply (-2 + y) * (-2 + y)
(-2(-2 + y) + y(-2 + y)) = 2y2 + 2y + 13
((-2 * -2 + y * -2) + y(-2 + y)) = 2y2 + 2y + 13
((4 + -2y) + y(-2 + y)) = 2y2 + 2y + 13
(4 + -2y + (-2 * y + y * y)) = 2y2 + 2y + 13
(4 + -2y + (-2y + y2)) = 2y2 + 2y + 13

Combine like terms: -2y + -2y = -4y
(4 + -4y + y2) = 2y2 + 2y + 13

Reorder the terms:
4 + -4y + y2 = 13 + 2y + 2y2

Solving
4 + -4y + y2 = 13 + 2y + 2y2

Solving for variable 'y'.

Reorder the terms:
4 + -13 + -4y + -2y + y2 + -2y2 = 13 + 2y + 2y2 + -13 + -2y + -2y2

Combine like terms: 4 + -13 = -9
-9 + -4y + -2y + y2 + -2y2 = 13 + 2y + 2y2 + -13 + -2y + -2y2

Combine like terms: -4y + -2y = -6y
-9 + -6y + y2 + -2y2 = 13 + 2y + 2y2 + -13 + -2y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-9 + -6y + -1y2 = 13 + 2y + 2y2 + -13 + -2y + -2y2

Reorder the terms:
-9 + -6y + -1y2 = 13 + -13 + 2y + -2y + 2y2 + -2y2

Combine like terms: 13 + -13 = 0
-9 + -6y + -1y2 = 0 + 2y + -2y + 2y2 + -2y2
-9 + -6y + -1y2 = 2y + -2y + 2y2 + -2y2

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

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

Factor out the Greatest Common Factor (GCF), '-1'.
-1(9 + 6y + y2) = 0

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

Ignore the factor -1.

Subproblem 1
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

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 = {-3, -3}

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