(y-1)(y-1)=2y^2-3y-11

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Solution for (y-1)(y-1)=2y^2-3y-11 equation: 


Simplifying
(y + -1)(y + -1) = 2y2 + -3y + -11

Reorder the terms:
(-1 + y)(y + -1) = 2y2 + -3y + -11

Reorder the terms:
(-1 + y)(-1 + y) = 2y2 + -3y + -11

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) = 2y2 + -3y + -11
((-1 * -1 + y * -1) + y(-1 + y)) = 2y2 + -3y + -11
((1 + -1y) + y(-1 + y)) = 2y2 + -3y + -11
(1 + -1y + (-1 * y + y * y)) = 2y2 + -3y + -11
(1 + -1y + (-1y + y2)) = 2y2 + -3y + -11

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) = 2y2 + -3y + -11

Reorder the terms:
1 + -2y + y2 = -11 + -3y + 2y2

Solving
1 + -2y + y2 = -11 + -3y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + 11 + -2y + 3y + y2 + -2y2 = -11 + -3y + 2y2 + 11 + 3y + -2y2

Combine like terms: 1 + 11 = 12
12 + -2y + 3y + y2 + -2y2 = -11 + -3y + 2y2 + 11 + 3y + -2y2

Combine like terms: -2y + 3y = 1y
12 + 1y + y2 + -2y2 = -11 + -3y + 2y2 + 11 + 3y + -2y2

Combine like terms: y2 + -2y2 = -1y2
12 + 1y + -1y2 = -11 + -3y + 2y2 + 11 + 3y + -2y2

Reorder the terms:
12 + 1y + -1y2 = -11 + 11 + -3y + 3y + 2y2 + -2y2

Combine like terms: -11 + 11 = 0
12 + 1y + -1y2 = 0 + -3y + 3y + 2y2 + -2y2
12 + 1y + -1y2 = -3y + 3y + 2y2 + -2y2

Combine like terms: -3y + 3y = 0
12 + 1y + -1y2 = 0 + 2y2 + -2y2
12 + 1y + -1y2 = 2y2 + -2y2

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

Factor a trinomial.
(4 + -1y)(3 + y) = 0


Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

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 = {4, -3}

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