(3y-2)(y-2)-y-3y-4=6y

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Solution for (3y-2)(y-2)-y-3y-4=6y equation:


Simplifying
(3y + -2)(y + -2) + -1y + -3y + -4 = 6y

Reorder the terms:
(-2 + 3y)(y + -2) + -1y + -3y + -4 = 6y

Reorder the terms:
(-2 + 3y)(-2 + y) + -1y + -3y + -4 = 6y

Multiply (-2 + 3y) * (-2 + y)
(-2(-2 + y) + 3y * (-2 + y)) + -1y + -3y + -4 = 6y
((-2 * -2 + y * -2) + 3y * (-2 + y)) + -1y + -3y + -4 = 6y
((4 + -2y) + 3y * (-2 + y)) + -1y + -3y + -4 = 6y
(4 + -2y + (-2 * 3y + y * 3y)) + -1y + -3y + -4 = 6y
(4 + -2y + (-6y + 3y2)) + -1y + -3y + -4 = 6y

Combine like terms: -2y + -6y = -8y
(4 + -8y + 3y2) + -1y + -3y + -4 = 6y

Reorder the terms:
4 + -4 + -8y + -1y + -3y + 3y2 = 6y

Combine like terms: 4 + -4 = 0
0 + -8y + -1y + -3y + 3y2 = 6y
-8y + -1y + -3y + 3y2 = 6y

Combine like terms: -8y + -1y = -9y
-9y + -3y + 3y2 = 6y

Combine like terms: -9y + -3y = -12y
-12y + 3y2 = 6y

Solving
-12y + 3y2 = 6y

Solving for variable 'y'.

Reorder the terms:
-12y + -6y + 3y2 = 6y + -6y

Combine like terms: -12y + -6y = -18y
-18y + 3y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-18y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3y'.
3y(-6 + y) = 0

Ignore the factor 3.

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 '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Solution
y = {0, 6}

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