6y^2+y=12

Solution for 6y^2+y=12 equation:

Simplifying
6y2 + y = 12

Reorder the terms:
y + 6y2 = 12

Solving
y + 6y2 = 12

Solving for variable 'y'.

Reorder the terms:
-12 + y + 6y2 = 12 + -12

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

Factor a trinomial.
(-3 + -2y)(4 + -3y) = 0

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 '(4 + -3y)' equal to zero and attempt to solve:

Simplifying
4 + -3y = 0

Solving
4 + -3y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3y = 0 + -4
-3y = 0 + -4

Combine like terms: 0 + -4 = -4
-3y = -4

Divide each side by '-3'.
y = 1.333333333

Simplifying
y = 1.333333333
Solution
y = {-1.5, 1.333333333}