2y^2-16y+30=(y-5)(y-5)

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Solution for 2y^2-16y+30=(y-5)(y-5) equation: 


Simplifying
2y2 + -16y + 30 = (y + -5)(y + -5)

Reorder the terms:
30 + -16y + 2y2 = (y + -5)(y + -5)

Reorder the terms:
30 + -16y + 2y2 = (-5 + y)(y + -5)

Reorder the terms:
30 + -16y + 2y2 = (-5 + y)(-5 + y)

Multiply (-5 + y) * (-5 + y)
30 + -16y + 2y2 = (-5(-5 + y) + y(-5 + y))
30 + -16y + 2y2 = ((-5 * -5 + y * -5) + y(-5 + y))
30 + -16y + 2y2 = ((25 + -5y) + y(-5 + y))
30 + -16y + 2y2 = (25 + -5y + (-5 * y + y * y))
30 + -16y + 2y2 = (25 + -5y + (-5y + y2))

Combine like terms: -5y + -5y = -10y
30 + -16y + 2y2 = (25 + -10y + y2)

Solving
30 + -16y + 2y2 = 25 + -10y + y2

Solving for variable 'y'.

Reorder the terms:
30 + -25 + -16y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: 30 + -25 = 5
5 + -16y + 10y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: -16y + 10y = -6y
5 + -6y + 2y2 + -1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
5 + -6y + 1y2 = 25 + -10y + y2 + -25 + 10y + -1y2

Reorder the terms:
5 + -6y + 1y2 = 25 + -25 + -10y + 10y + y2 + -1y2

Combine like terms: 25 + -25 = 0
5 + -6y + 1y2 = 0 + -10y + 10y + y2 + -1y2
5 + -6y + 1y2 = -10y + 10y + y2 + -1y2

Combine like terms: -10y + 10y = 0
5 + -6y + 1y2 = 0 + y2 + -1y2
5 + -6y + 1y2 = y2 + -1y2

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

Factor a trinomial.
(1 + -1y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {1, 5}

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