(y+2)(2y-4)=3y(y-2)

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Solution for (y+2)(2y-4)=3y(y-2) equation: 


Simplifying
(y + 2)(2y + -4) = 3y(y + -2)

Reorder the terms:
(2 + y)(2y + -4) = 3y(y + -2)

Reorder the terms:
(2 + y)(-4 + 2y) = 3y(y + -2)

Multiply (2 + y) * (-4 + 2y)
(2(-4 + 2y) + y(-4 + 2y)) = 3y(y + -2)
((-4 * 2 + 2y * 2) + y(-4 + 2y)) = 3y(y + -2)
((-8 + 4y) + y(-4 + 2y)) = 3y(y + -2)
(-8 + 4y + (-4 * y + 2y * y)) = 3y(y + -2)
(-8 + 4y + (-4y + 2y2)) = 3y(y + -2)

Combine like terms: 4y + -4y = 0
(-8 + 0 + 2y2) = 3y(y + -2)
(-8 + 2y2) = 3y(y + -2)

Reorder the terms:
-8 + 2y2 = 3y(-2 + y)
-8 + 2y2 = (-2 * 3y + y * 3y)
-8 + 2y2 = (-6y + 3y2)

Solving
-8 + 2y2 = -6y + 3y2

Solving for variable 'y'.

Reorder the terms:
-8 + 6y + 2y2 + -3y2 = -6y + 3y2 + 6y + -3y2

Combine like terms: 2y2 + -3y2 = -1y2
-8 + 6y + -1y2 = -6y + 3y2 + 6y + -3y2

Reorder the terms:
-8 + 6y + -1y2 = -6y + 6y + 3y2 + -3y2

Combine like terms: -6y + 6y = 0
-8 + 6y + -1y2 = 0 + 3y2 + -3y2
-8 + 6y + -1y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
-8 + 6y + -1y2 = 0

Factor a trinomial.
(-4 + y)(2 + -1y) = 0


Subproblem 1
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 0

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

Add '4' to each side of the equation.
-4 + 4 + y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + y = 0 + 4
y = 0 + 4

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4

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 = {4, 2}

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