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

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Solution for -6y-2y(y+1)=3(y-2)+6 equation: 


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

Reorder the terms:
-6y + -2y(1 + y) = 3(y + -2) + 6
-6y + (1 * -2y + y * -2y) = 3(y + -2) + 6
-6y + (-2y + -2y2) = 3(y + -2) + 6

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

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

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

Combine like terms: -6 + 6 = 0
-8y + -2y2 = 0 + 3y
-8y + -2y2 = 3y

Solving
-8y + -2y2 = 3y

Solving for variable 'y'.

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

Combine like terms: -8y + -3y = -11y
-11y + -2y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-11y + -2y2 = 0

Factor out the Greatest Common Factor (GCF), '-1y'.
-1y(11 + 2y) = 0

Ignore the factor -1.

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 '(11 + 2y)' equal to zero and attempt to solve:

Simplifying
11 + 2y = 0

Solving
11 + 2y = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2y = 0 + -11
2y = 0 + -11

Combine like terms: 0 + -11 = -11
2y = -11

Divide each side by '2'.
y = -5.5

Simplifying
y = -5.5
Solution
y = {0, -5.5}

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