y(y-2)(y-2)=0

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Solution for y(y-2)(y-2)=0 equation: 


Simplifying
y(y + -2)(y + -2) = 0

Reorder the terms:
y(-2 + y)(y + -2) = 0

Reorder the terms:
y(-2 + y)(-2 + y) = 0

Multiply (-2 + y) * (-2 + y)
y(-2(-2 + y) + y(-2 + y)) = 0
y((-2 * -2 + y * -2) + y(-2 + y)) = 0
y((4 + -2y) + y(-2 + y)) = 0
y(4 + -2y + (-2 * y + y * y)) = 0
y(4 + -2y + (-2y + y2)) = 0

Combine like terms: -2y + -2y = -4y
y(4 + -4y + y2) = 0
(4 * y + -4y * y + y2 * y) = 0
(4y + -4y2 + y3) = 0

Solving
4y + -4y2 + y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), 'y'.
y(4 + -4y + y2) = 0

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


Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0

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

Subproblem 3
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 = {0, 2, 2}

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