2y^2-13y+6+y-6+y-6=0

Solution for 2y^2-13y+6+y-6+y-6=0 equation:

Simplifying
2y2 + -13y + 6 + y + -6 + y + -6 = 0

Reorder the terms:
6 + -6 + -6 + -13y + y + y + 2y2 = 0

Combine like terms: 6 + -6 = 0
0 + -6 + -13y + y + y + 2y2 = 0
-6 + -13y + y + y + 2y2 = 0

Combine like terms: -13y + y = -12y
-6 + -12y + y + 2y2 = 0

Combine like terms: -12y + y = -11y
-6 + -11y + 2y2 = 0

Solving
-6 + -11y + 2y2 = 0

Solving for variable 'y'.

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

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 '(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 = {-0.5, 6}