2y^2-11y+23=(y-5)(y-5)

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Solution for 2y^2-11y+23=(y-5)(y-5) equation: 


Simplifying
2y2 + -11y + 23 = (y + -5)(y + -5)

Reorder the terms:
23 + -11y + 2y2 = (y + -5)(y + -5)

Reorder the terms:
23 + -11y + 2y2 = (-5 + y)(y + -5)

Reorder the terms:
23 + -11y + 2y2 = (-5 + y)(-5 + y)

Multiply (-5 + y) * (-5 + y)
23 + -11y + 2y2 = (-5(-5 + y) + y(-5 + y))
23 + -11y + 2y2 = ((-5 * -5 + y * -5) + y(-5 + y))
23 + -11y + 2y2 = ((25 + -5y) + y(-5 + y))
23 + -11y + 2y2 = (25 + -5y + (-5 * y + y * y))
23 + -11y + 2y2 = (25 + -5y + (-5y + y2))

Combine like terms: -5y + -5y = -10y
23 + -11y + 2y2 = (25 + -10y + y2)

Solving
23 + -11y + 2y2 = 25 + -10y + y2

Solving for variable 'y'.

Reorder the terms:
23 + -25 + -11y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: 23 + -25 = -2
-2 + -11y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: -11y + 10y = -1y
-2 + -1y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

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

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

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

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

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

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

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