(3y-9)(12y+2)=0

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Solution for (3y-9)(12y+2)=0 equation: 


Simplifying
(3y + -9)(12y + 2) = 0

Reorder the terms:
(-9 + 3y)(12y + 2) = 0

Reorder the terms:
(-9 + 3y)(2 + 12y) = 0

Multiply (-9 + 3y) * (2 + 12y)
(-9(2 + 12y) + 3y * (2 + 12y)) = 0
((2 * -9 + 12y * -9) + 3y * (2 + 12y)) = 0
((-18 + -108y) + 3y * (2 + 12y)) = 0
(-18 + -108y + (2 * 3y + 12y * 3y)) = 0
(-18 + -108y + (6y + 36y2)) = 0

Combine like terms: -108y + 6y = -102y
(-18 + -102y + 36y2) = 0

Solving
-18 + -102y + 36y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -17y + 6y2) = 0

Factor a trinomial.
6((-1 + -6y)(3 + -1y)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-1 + -6y)' equal to zero and attempt to solve:

Simplifying
-1 + -6y = 0

Solving
-1 + -6y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -6y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6y = 0 + 1
-6y = 0 + 1

Combine like terms: 0 + 1 = 1
-6y = 1

Divide each side by '-6'.
y = -0.1666666667

Simplifying
y = -0.1666666667

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-0.1666666667, 3}

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