(y-3)(y-3)=2y^2-5y+3

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Solution for (y-3)(y-3)=2y^2-5y+3 equation: 


Simplifying
(y + -3)(y + -3) = 2y2 + -5y + 3

Reorder the terms:
(-3 + y)(y + -3) = 2y2 + -5y + 3

Reorder the terms:
(-3 + y)(-3 + y) = 2y2 + -5y + 3

Multiply (-3 + y) * (-3 + y)
(-3(-3 + y) + y(-3 + y)) = 2y2 + -5y + 3
((-3 * -3 + y * -3) + y(-3 + y)) = 2y2 + -5y + 3
((9 + -3y) + y(-3 + y)) = 2y2 + -5y + 3
(9 + -3y + (-3 * y + y * y)) = 2y2 + -5y + 3
(9 + -3y + (-3y + y2)) = 2y2 + -5y + 3

Combine like terms: -3y + -3y = -6y
(9 + -6y + y2) = 2y2 + -5y + 3

Reorder the terms:
9 + -6y + y2 = 3 + -5y + 2y2

Solving
9 + -6y + y2 = 3 + -5y + 2y2

Solving for variable 'y'.

Reorder the terms:
9 + -3 + -6y + 5y + y2 + -2y2 = 3 + -5y + 2y2 + -3 + 5y + -2y2

Combine like terms: 9 + -3 = 6
6 + -6y + 5y + y2 + -2y2 = 3 + -5y + 2y2 + -3 + 5y + -2y2

Combine like terms: -6y + 5y = -1y
6 + -1y + y2 + -2y2 = 3 + -5y + 2y2 + -3 + 5y + -2y2

Combine like terms: y2 + -2y2 = -1y2
6 + -1y + -1y2 = 3 + -5y + 2y2 + -3 + 5y + -2y2

Reorder the terms:
6 + -1y + -1y2 = 3 + -3 + -5y + 5y + 2y2 + -2y2

Combine like terms: 3 + -3 = 0
6 + -1y + -1y2 = 0 + -5y + 5y + 2y2 + -2y2
6 + -1y + -1y2 = -5y + 5y + 2y2 + -2y2

Combine like terms: -5y + 5y = 0
6 + -1y + -1y2 = 0 + 2y2 + -2y2
6 + -1y + -1y2 = 2y2 + -2y2

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

Factor a trinomial.
(2 + -1y)(3 + y) = 0


Subproblem 1
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

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 = {2, -3}

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