(y-3)(y-3)=2y^2-12y+17

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Solution for (y-3)(y-3)=2y^2-12y+17 equation: 


Simplifying
(y + -3)(y + -3) = 2y2 + -12y + 17

Reorder the terms:
(-3 + y)(y + -3) = 2y2 + -12y + 17

Reorder the terms:
(-3 + y)(-3 + y) = 2y2 + -12y + 17

Multiply (-3 + y) * (-3 + y)
(-3(-3 + y) + y(-3 + y)) = 2y2 + -12y + 17
((-3 * -3 + y * -3) + y(-3 + y)) = 2y2 + -12y + 17
((9 + -3y) + y(-3 + y)) = 2y2 + -12y + 17
(9 + -3y + (-3 * y + y * y)) = 2y2 + -12y + 17
(9 + -3y + (-3y + y2)) = 2y2 + -12y + 17

Combine like terms: -3y + -3y = -6y
(9 + -6y + y2) = 2y2 + -12y + 17

Reorder the terms:
9 + -6y + y2 = 17 + -12y + 2y2

Solving
9 + -6y + y2 = 17 + -12y + 2y2

Solving for variable 'y'.

Reorder the terms:
9 + -17 + -6y + 12y + y2 + -2y2 = 17 + -12y + 2y2 + -17 + 12y + -2y2

Combine like terms: 9 + -17 = -8
-8 + -6y + 12y + y2 + -2y2 = 17 + -12y + 2y2 + -17 + 12y + -2y2

Combine like terms: -6y + 12y = 6y
-8 + 6y + y2 + -2y2 = 17 + -12y + 2y2 + -17 + 12y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-8 + 6y + -1y2 = 17 + -12y + 2y2 + -17 + 12y + -2y2

Reorder the terms:
-8 + 6y + -1y2 = 17 + -17 + -12y + 12y + 2y2 + -2y2

Combine like terms: 17 + -17 = 0
-8 + 6y + -1y2 = 0 + -12y + 12y + 2y2 + -2y2
-8 + 6y + -1y2 = -12y + 12y + 2y2 + -2y2

Combine like terms: -12y + 12y = 0
-8 + 6y + -1y2 = 0 + 2y2 + -2y2
-8 + 6y + -1y2 = 2y2 + -2y2

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

Factor a trinomial.
(-4 + y)(2 + -1y) = 0


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

Simplifying
-4 + y = 0

Solving
-4 + y = 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 + y = 0 + 4

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

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

Simplifying
y = 4

Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 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 + -1y = 0 + -2

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

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

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {4, 2}

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