3Y^2-5=2Y

Solution for 3Y^2-5=2Y equation:

Simplifying
3Y2 + -5 = 2Y

Reorder the terms:
-5 + 3Y2 = 2Y

Solving
-5 + 3Y2 = 2Y

Solving for variable 'Y'.

Reorder the terms:
-5 + -2Y + 3Y2 = 2Y + -2Y

Combine like terms: 2Y + -2Y = 0
-5 + -2Y + 3Y2 = 0

Factor a trinomial.
(-1 + -1Y)(5 + -3Y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3Y)' equal to zero and attempt to solve:

Simplifying
5 + -3Y = 0

Solving
5 + -3Y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3Y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3Y = 0 + -5
-3Y = 0 + -5

Combine like terms: 0 + -5 = -5
-3Y = -5

Divide each side by '-3'.
Y = 1.666666667

Simplifying
Y = 1.666666667
Solution
Y = {-1, 1.666666667}