(3y+6)(3y-2)=0

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Solution for (3y+6)(3y-2)=0 equation: 


Simplifying
(3y + 6)(3y + -2) = 0

Reorder the terms:
(6 + 3y)(3y + -2) = 0

Reorder the terms:
(6 + 3y)(-2 + 3y) = 0

Multiply (6 + 3y) * (-2 + 3y)
(6(-2 + 3y) + 3y * (-2 + 3y)) = 0
((-2 * 6 + 3y * 6) + 3y * (-2 + 3y)) = 0
((-12 + 18y) + 3y * (-2 + 3y)) = 0
(-12 + 18y + (-2 * 3y + 3y * 3y)) = 0
(-12 + 18y + (-6y + 9y2)) = 0

Combine like terms: 18y + -6y = 12y
(-12 + 12y + 9y2) = 0

Solving
-12 + 12y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 4y + 3y2) = 0

Factor a trinomial.
3((-2 + -1y)(2 + -3y)) = 0

Ignore the factor 3.

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 '(2 + -3y)' equal to zero and attempt to solve:

Simplifying
2 + -3y = 0

Solving
2 + -3y = 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 + -3y = 0 + -2

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

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

Divide each side by '-3'.
y = 0.6666666667

Simplifying
y = 0.6666666667
Solution
y = {-2, 0.6666666667}

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