6y^2=9y-3

Solution for 6y^2=9y-3 equation:

Simplifying
6y2 = 9y + -3

Reorder the terms:
6y2 = -3 + 9y

Solving
6y2 = -3 + 9y

Solving for variable 'y'.

Reorder the terms:
3 + -9y + 6y2 = -3 + 9y + 3 + -9y

Reorder the terms:
3 + -9y + 6y2 = -3 + 3 + 9y + -9y

Combine like terms: -3 + 3 = 0
3 + -9y + 6y2 = 0 + 9y + -9y
3 + -9y + 6y2 = 9y + -9y

Combine like terms: 9y + -9y = 0
3 + -9y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -3y + 2y2) = 0

Factor a trinomial.
3((1 + -2y)(1 + -1y)) = 0

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 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 + -2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2y = 0 + -1
-2y = 0 + -1

Combine like terms: 0 + -1 = -1
-2y = -1

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
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 = {0.5, 1}