[y-2(y-5)][y-2(y-5)]=0

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Solution for [y-2(y-5)][y-2(y-5)]=0 equation: 


Simplifying
[y + -2(y + -5)][y + -2(y + -5)] = 0

Reorder the terms:
[y + -2(-5 + y)][y + -2(y + -5)] = 0
[y + (-5 * -2 + y * -2)][y + -2(y + -5)] = 0
[y + (10 + -2y)][y + -2(y + -5)] = 0

Reorder the terms:
[10 + y + -2y][y + -2(y + -5)] = 0

Combine like terms: y + -2y = -1y
[10 + -1y][y + -2(y + -5)] = 0

Reorder the terms:
[10 + -1y][y + -2(-5 + y)] = 0
[10 + -1y][y + (-5 * -2 + y * -2)] = 0
[10 + -1y][y + (10 + -2y)] = 0

Reorder the terms:
[10 + -1y][10 + y + -2y] = 0

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

Multiply [10 + -1y] * [10 + -1y]
[10[10 + -1y] + -1y * [10 + -1y]] = 0
[[10 * 10 + -1y * 10] + -1y * [10 + -1y]] = 0
[[100 + -10y] + -1y * [10 + -1y]] = 0
[100 + -10y + [10 * -1y + -1y * -1y]] = 0
[100 + -10y + [-10y + 1y2]] = 0

Combine like terms: -10y + -10y = -20y
[100 + -20y + 1y2] = 0

Solving
100 + -20y + 1y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(10 + -1y)(10 + -1y) = 0


Subproblem 1
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

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

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

Divide each side by '-1'.
y = 10

Simplifying
y = 10

Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

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

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

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {10, 10}

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