3y^2-5y+8=9y^2-10y+2

Solution for 3y^2-5y+8=9y^2-10y+2 equation:

Simplifying
3y2 + -5y + 8 = 9y2 + -10y + 2

Reorder the terms:
8 + -5y + 3y2 = 9y2 + -10y + 2

Reorder the terms:
8 + -5y + 3y2 = 2 + -10y + 9y2

Solving
8 + -5y + 3y2 = 2 + -10y + 9y2

Solving for variable 'y'.

Reorder the terms:
8 + -2 + -5y + 10y + 3y2 + -9y2 = 2 + -10y + 9y2 + -2 + 10y + -9y2

Combine like terms: 8 + -2 = 6
6 + -5y + 10y + 3y2 + -9y2 = 2 + -10y + 9y2 + -2 + 10y + -9y2

Combine like terms: -5y + 10y = 5y
6 + 5y + 3y2 + -9y2 = 2 + -10y + 9y2 + -2 + 10y + -9y2

Combine like terms: 3y2 + -9y2 = -6y2
6 + 5y + -6y2 = 2 + -10y + 9y2 + -2 + 10y + -9y2

Reorder the terms:
6 + 5y + -6y2 = 2 + -2 + -10y + 10y + 9y2 + -9y2

Combine like terms: 2 + -2 = 0
6 + 5y + -6y2 = 0 + -10y + 10y + 9y2 + -9y2
6 + 5y + -6y2 = -10y + 10y + 9y2 + -9y2

Combine like terms: -10y + 10y = 0
6 + 5y + -6y2 = 0 + 9y2 + -9y2
6 + 5y + -6y2 = 9y2 + -9y2

Combine like terms: 9y2 + -9y2 = 0
6 + 5y + -6y2 = 0

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

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

Simplifying
3 + -2y = 0

Solving
3 + -2y = 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 + -2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2y = 0 + -3
-2y = 0 + -3

Combine like terms: 0 + -3 = -3
-2y = -3

Divide each side by '-2'.
y = 1.5

Simplifying
y = 1.5
Subproblem 2
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
Solution
y = {1.5, -0.6666666667}