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

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


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

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

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

Multiply (-9 + 2y) * (2 + 3y)
(-9(2 + 3y) + 2y * (2 + 3y)) = 0
((2 * -9 + 3y * -9) + 2y * (2 + 3y)) = 0
((-18 + -27y) + 2y * (2 + 3y)) = 0
(-18 + -27y + (2 * 2y + 3y * 2y)) = 0
(-18 + -27y + (4y + 6y2)) = 0

Combine like terms: -27y + 4y = -23y
(-18 + -23y + 6y2) = 0

Solving
-18 + -23y + 6y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -3y)(9 + -2y) = 0


Subproblem 1
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

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

Simplifying
9 + -2y = 0

Solving
9 + -2y = 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 + -2y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2y = 0 + -9
-2y = 0 + -9

Combine like terms: 0 + -9 = -9
-2y = -9

Divide each side by '-2'.
y = 4.5

Simplifying
y = 4.5
Solution
y = {-0.6666666667, 4.5}

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