2y^2-17y+45=(y-7)(y-7)

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Solution for 2y^2-17y+45=(y-7)(y-7) equation: 


Simplifying
2y2 + -17y + 45 = (y + -7)(y + -7)

Reorder the terms:
45 + -17y + 2y2 = (y + -7)(y + -7)

Reorder the terms:
45 + -17y + 2y2 = (-7 + y)(y + -7)

Reorder the terms:
45 + -17y + 2y2 = (-7 + y)(-7 + y)

Multiply (-7 + y) * (-7 + y)
45 + -17y + 2y2 = (-7(-7 + y) + y(-7 + y))
45 + -17y + 2y2 = ((-7 * -7 + y * -7) + y(-7 + y))
45 + -17y + 2y2 = ((49 + -7y) + y(-7 + y))
45 + -17y + 2y2 = (49 + -7y + (-7 * y + y * y))
45 + -17y + 2y2 = (49 + -7y + (-7y + y2))

Combine like terms: -7y + -7y = -14y
45 + -17y + 2y2 = (49 + -14y + y2)

Solving
45 + -17y + 2y2 = 49 + -14y + y2

Solving for variable 'y'.

Reorder the terms:
45 + -49 + -17y + 14y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 45 + -49 = -4
-4 + -17y + 14y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: -17y + 14y = -3y
-4 + -3y + 2y2 + -1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-4 + -3y + 1y2 = 49 + -14y + y2 + -49 + 14y + -1y2

Reorder the terms:
-4 + -3y + 1y2 = 49 + -49 + -14y + 14y + y2 + -1y2

Combine like terms: 49 + -49 = 0
-4 + -3y + 1y2 = 0 + -14y + 14y + y2 + -1y2
-4 + -3y + 1y2 = -14y + 14y + y2 + -1y2

Combine like terms: -14y + 14y = 0
-4 + -3y + 1y2 = 0 + y2 + -1y2
-4 + -3y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-4 + -3y + 1y2 = 0

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


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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1

Subproblem 2
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
Solution
y = {-1, 4}

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