(3y-27)(2y+8)=0

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Solution for (3y-27)(2y+8)=0 equation: 


Simplifying
(3y + -27)(2y + 8) = 0

Reorder the terms:
(-27 + 3y)(2y + 8) = 0

Reorder the terms:
(-27 + 3y)(8 + 2y) = 0

Multiply (-27 + 3y) * (8 + 2y)
(-27(8 + 2y) + 3y * (8 + 2y)) = 0
((8 * -27 + 2y * -27) + 3y * (8 + 2y)) = 0
((-216 + -54y) + 3y * (8 + 2y)) = 0
(-216 + -54y + (8 * 3y + 2y * 3y)) = 0
(-216 + -54y + (24y + 6y2)) = 0

Combine like terms: -54y + 24y = -30y
(-216 + -30y + 6y2) = 0

Solving
-216 + -30y + 6y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-36 + -5y + y2) = 0

Factor a trinomial.
6((-4 + -1y)(9 + -1y)) = 0

Ignore the factor 6.

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

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 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 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4

Subproblem 2
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-4, 9}

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