9y^2-54y=-81

Solution for 9y^2-54y=-81 equation:

Simplifying
9y2 + -54y = -81

Reorder the terms:
-54y + 9y2 = -81

Solving
-54y + 9y2 = -81

Solving for variable 'y'.

Reorder the terms:
81 + -54y + 9y2 = -81 + 81

Combine like terms: -81 + 81 = 0
81 + -54y + 9y2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(9 + -6y + y2) = 0

Factor a trinomial.
9((3 + -1y)(3 + -1y)) = 0

Ignore the factor 9.
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 '(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
Solution
y = {3, 3}