6y^2-5y=11

Solution for 6y^2-5y=11 equation:

Simplifying
6y2 + -5y = 11

Reorder the terms:
-5y + 6y2 = 11

Solving
-5y + 6y2 = 11

Solving for variable 'y'.

Reorder the terms:
-11 + -5y + 6y2 = 11 + -11

Combine like terms: 11 + -11 = 0
-11 + -5y + 6y2 = 0

Factor a trinomial.
(-1 + -1y)(11 + -6y) = 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 '(11 + -6y)' equal to zero and attempt to solve:

Simplifying
11 + -6y = 0

Solving
11 + -6y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -6y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -6y = 0 + -11
-6y = 0 + -11

Combine like terms: 0 + -11 = -11
-6y = -11

Divide each side by '-6'.
y = 1.833333333

Simplifying
y = 1.833333333
Solution
y = {-1, 1.833333333}