2y^2-12y+17=(y-5)(y-5)

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Solution for 2y^2-12y+17=(y-5)(y-5) equation: 


Simplifying
2y2 + -12y + 17 = (y + -5)(y + -5)

Reorder the terms:
17 + -12y + 2y2 = (y + -5)(y + -5)

Reorder the terms:
17 + -12y + 2y2 = (-5 + y)(y + -5)

Reorder the terms:
17 + -12y + 2y2 = (-5 + y)(-5 + y)

Multiply (-5 + y) * (-5 + y)
17 + -12y + 2y2 = (-5(-5 + y) + y(-5 + y))
17 + -12y + 2y2 = ((-5 * -5 + y * -5) + y(-5 + y))
17 + -12y + 2y2 = ((25 + -5y) + y(-5 + y))
17 + -12y + 2y2 = (25 + -5y + (-5 * y + y * y))
17 + -12y + 2y2 = (25 + -5y + (-5y + y2))

Combine like terms: -5y + -5y = -10y
17 + -12y + 2y2 = (25 + -10y + y2)

Solving
17 + -12y + 2y2 = 25 + -10y + y2

Solving for variable 'y'.

Reorder the terms:
17 + -25 + -12y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: 17 + -25 = -8
-8 + -12y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: -12y + 10y = -2y
-8 + -2y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-8 + -2y + 1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Reorder the terms:
-8 + -2y + 1y2 = 25 + -25 + -10y + 10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
-8 + -2y + 1y2 = 0 + -10y + 10y + y2 + -1y2
-8 + -2y + 1y2 = -10y + 10y + y2 + -1y2

Combine like terms: -10y + 10y = 0
-8 + -2y + 1y2 = 0 + y2 + -1y2
-8 + -2y + 1y2 = y2 + -1y2

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

Factor a trinomial.
(-2 + -1y)(4 + -1y) = 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 '(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 = {-2, 4}

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