3Y^2+8Y+-9=2Y

Solution for 3Y^2+8Y+-9=2Y equation:

Simplifying
3Y2 + 8Y + -9 = 2Y

Reorder the terms:
-9 + 8Y + 3Y2 = 2Y

Solving
-9 + 8Y + 3Y2 = 2Y

Solving for variable 'Y'.

Reorder the terms:
-9 + 8Y + -2Y + 3Y2 = 2Y + -2Y

Combine like terms: 8Y + -2Y = 6Y
-9 + 6Y + 3Y2 = 2Y + -2Y

Combine like terms: 2Y + -2Y = 0
-9 + 6Y + 3Y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 2Y + Y2) = 0

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

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

Simplifying
1 + -1Y = 0

Solving
1 + -1Y = 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 + -1Y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1Y = 0 + -1
-1Y = 0 + -1

Combine like terms: 0 + -1 = -1
-1Y = -1

Divide each side by '-1'.
Y = 1

Simplifying
Y = 1
Solution
Y = {-3, 1}