[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 = 3y
[10 + -1y][-10 + 3y] = 0

Multiply [10 + -1y] * [-10 + 3y]
[10[-10 + 3y] + -1y * [-10 + 3y]] = 0
[[-10 * 10 + 3y * 10] + -1y * [-10 + 3y]] = 0
[[-100 + 30y] + -1y * [-10 + 3y]] = 0
[-100 + 30y + [-10 * -1y + 3y * -1y]] = 0
[-100 + 30y + [10y + -3y2]] = 0

Combine like terms: 30y + 10y = 40y
[-100 + 40y + -3y2] = 0

Solving
-100 + 40y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-10 + y)(10 + -3y) = 0


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

Simplifying
-10 + y = 0

Solving
-10 + y = 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 + y = 0 + 10

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

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

Simplifying
y = 10

Subproblem 2
Set the factor '(10 + -3y)' equal to zero and attempt to solve:

Simplifying
10 + -3y = 0

Solving
10 + -3y = 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 + -3y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3y = 0 + -10
-3y = 0 + -10

Combine like terms: 0 + -10 = -10
-3y = -10

Divide each side by '-3'.
y = 3.333333333

Simplifying
y = 3.333333333
Solution
y = {10, 3.333333333}

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