2y^2-10y+8=(y-4)(y-4)

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Solution for 2y^2-10y+8=(y-4)(y-4) equation: 


Simplifying
2y2 + -10y + 8 = (y + -4)(y + -4)

Reorder the terms:
8 + -10y + 2y2 = (y + -4)(y + -4)

Reorder the terms:
8 + -10y + 2y2 = (-4 + y)(y + -4)

Reorder the terms:
8 + -10y + 2y2 = (-4 + y)(-4 + y)

Multiply (-4 + y) * (-4 + y)
8 + -10y + 2y2 = (-4(-4 + y) + y(-4 + y))
8 + -10y + 2y2 = ((-4 * -4 + y * -4) + y(-4 + y))
8 + -10y + 2y2 = ((16 + -4y) + y(-4 + y))
8 + -10y + 2y2 = (16 + -4y + (-4 * y + y * y))
8 + -10y + 2y2 = (16 + -4y + (-4y + y2))

Combine like terms: -4y + -4y = -8y
8 + -10y + 2y2 = (16 + -8y + y2)

Solving
8 + -10y + 2y2 = 16 + -8y + y2

Solving for variable 'y'.

Reorder the terms:
8 + -16 + -10y + 8y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: 8 + -16 = -8
-8 + -10y + 8y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: -10y + 8y = -2y
-8 + -2y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-8 + -2y + 1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Reorder the terms:
-8 + -2y + 1y2 = 16 + -16 + -8y + 8y + y2 + -1y2

Combine like terms: 16 + -16 = 0
-8 + -2y + 1y2 = 0 + -8y + 8y + y2 + -1y2
-8 + -2y + 1y2 = -8y + 8y + y2 + -1y2

Combine like terms: -8y + 8y = 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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