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

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


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

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

Reorder the terms:
-4y + y2 = 2(8 + y)
-4y + y2 = (8 * 2 + y * 2)
-4y + y2 = (16 + 2y)

Solving
-4y + y2 = 16 + 2y

Solving for variable 'y'.

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

Combine like terms: -4y + -2y = -6y
-16 + -6y + y2 = 16 + 2y + -16 + -2y

Reorder the terms:
-16 + -6y + y2 = 16 + -16 + 2y + -2y

Combine like terms: 16 + -16 = 0
-16 + -6y + y2 = 0 + 2y + -2y
-16 + -6y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-16 + -6y + y2 = 0

Factor a trinomial.
(-2 + -1y)(8 + -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 '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-2, 8}

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