(y-1)(y-1)=2y^2+6y+16

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Solution for (y-1)(y-1)=2y^2+6y+16 equation: 


Simplifying
(y + -1)(y + -1) = 2y2 + 6y + 16

Reorder the terms:
(-1 + y)(y + -1) = 2y2 + 6y + 16

Reorder the terms:
(-1 + y)(-1 + y) = 2y2 + 6y + 16

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) = 2y2 + 6y + 16
((-1 * -1 + y * -1) + y(-1 + y)) = 2y2 + 6y + 16
((1 + -1y) + y(-1 + y)) = 2y2 + 6y + 16
(1 + -1y + (-1 * y + y * y)) = 2y2 + 6y + 16
(1 + -1y + (-1y + y2)) = 2y2 + 6y + 16

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) = 2y2 + 6y + 16

Reorder the terms:
1 + -2y + y2 = 16 + 6y + 2y2

Solving
1 + -2y + y2 = 16 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + -16 + -2y + -6y + y2 + -2y2 = 16 + 6y + 2y2 + -16 + -6y + -2y2

Combine like terms: 1 + -16 = -15
-15 + -2y + -6y + y2 + -2y2 = 16 + 6y + 2y2 + -16 + -6y + -2y2

Combine like terms: -2y + -6y = -8y
-15 + -8y + y2 + -2y2 = 16 + 6y + 2y2 + -16 + -6y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-15 + -8y + -1y2 = 16 + 6y + 2y2 + -16 + -6y + -2y2

Reorder the terms:
-15 + -8y + -1y2 = 16 + -16 + 6y + -6y + 2y2 + -2y2

Combine like terms: 16 + -16 = 0
-15 + -8y + -1y2 = 0 + 6y + -6y + 2y2 + -2y2
-15 + -8y + -1y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
-15 + -8y + -1y2 = 0 + 2y2 + -2y2
-15 + -8y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-15 + -8y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 8y + y2) = 0

Factor a trinomial.
-1((5 + y)(3 + 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 '(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 = {-5, -3}

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