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

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


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

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

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

Multiply (-2 + y) * (-2 + y)
y2 + (-2(-2 + y) + y(-2 + y)) = (y + -4)(y + -4)
y2 + ((-2 * -2 + y * -2) + y(-2 + y)) = (y + -4)(y + -4)
y2 + ((4 + -2y) + y(-2 + y)) = (y + -4)(y + -4)
y2 + (4 + -2y + (-2 * y + y * y)) = (y + -4)(y + -4)
y2 + (4 + -2y + (-2y + y2)) = (y + -4)(y + -4)

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

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

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

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

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

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

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

Solving
4 + -4y + 2y2 = 16 + -8y + y2

Solving for variable 'y'.

Reorder the terms:
4 + -16 + -4y + 8y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: 4 + -16 = -12
-12 + -4y + 8y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: -4y + 8y = 4y
-12 + 4y + 2y2 + -1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-12 + 4y + 1y2 = 16 + -8y + y2 + -16 + 8y + -1y2

Reorder the terms:
-12 + 4y + 1y2 = 16 + -16 + -8y + 8y + y2 + -1y2

Combine like terms: 16 + -16 = 0
-12 + 4y + 1y2 = 0 + -8y + 8y + y2 + -1y2
-12 + 4y + 1y2 = -8y + 8y + y2 + -1y2

Combine like terms: -8y + 8y = 0
-12 + 4y + 1y2 = 0 + y2 + -1y2
-12 + 4y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-12 + 4y + 1y2 = 0

Factor a trinomial.
(-6 + -1y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

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

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

Divide each side by '-1'.
y = -6

Simplifying
y = -6

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 = {-6, 2}

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