(y-1)(y-1)=2y^2-5y-9

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Solution for (y-1)(y-1)=2y^2-5y-9 equation: 


Simplifying
(y + -1)(y + -1) = 2y2 + -5y + -9

Reorder the terms:
(-1 + y)(y + -1) = 2y2 + -5y + -9

Reorder the terms:
(-1 + y)(-1 + y) = 2y2 + -5y + -9

Multiply (-1 + y) * (-1 + y)
(-1(-1 + y) + y(-1 + y)) = 2y2 + -5y + -9
((-1 * -1 + y * -1) + y(-1 + y)) = 2y2 + -5y + -9
((1 + -1y) + y(-1 + y)) = 2y2 + -5y + -9
(1 + -1y + (-1 * y + y * y)) = 2y2 + -5y + -9
(1 + -1y + (-1y + y2)) = 2y2 + -5y + -9

Combine like terms: -1y + -1y = -2y
(1 + -2y + y2) = 2y2 + -5y + -9

Reorder the terms:
1 + -2y + y2 = -9 + -5y + 2y2

Solving
1 + -2y + y2 = -9 + -5y + 2y2

Solving for variable 'y'.

Reorder the terms:
1 + 9 + -2y + 5y + y2 + -2y2 = -9 + -5y + 2y2 + 9 + 5y + -2y2

Combine like terms: 1 + 9 = 10
10 + -2y + 5y + y2 + -2y2 = -9 + -5y + 2y2 + 9 + 5y + -2y2

Combine like terms: -2y + 5y = 3y
10 + 3y + y2 + -2y2 = -9 + -5y + 2y2 + 9 + 5y + -2y2

Combine like terms: y2 + -2y2 = -1y2
10 + 3y + -1y2 = -9 + -5y + 2y2 + 9 + 5y + -2y2

Reorder the terms:
10 + 3y + -1y2 = -9 + 9 + -5y + 5y + 2y2 + -2y2

Combine like terms: -9 + 9 = 0
10 + 3y + -1y2 = 0 + -5y + 5y + 2y2 + -2y2
10 + 3y + -1y2 = -5y + 5y + 2y2 + -2y2

Combine like terms: -5y + 5y = 0
10 + 3y + -1y2 = 0 + 2y2 + -2y2
10 + 3y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
10 + 3y + -1y2 = 0

Factor a trinomial.
(5 + -1y)(2 + 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 '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {5, -2}

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