6y^2-27y=54

Solution for 6y^2-27y=54 equation:

Simplifying
6y2 + -27y = 54

Reorder the terms:
-27y + 6y2 = 54

Solving
-27y + 6y2 = 54

Solving for variable 'y'.

Reorder the terms:
-54 + -27y + 6y2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -27y + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-18 + -9y + 2y2) = 0

Factor a trinomial.
3((-3 + -2y)(6 + -1y)) = 0

Ignore the factor 3.
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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-1.5, 6}