4y-3y^2+6=y

Solution for 4y-3y^2+6=y equation:

Simplifying
4y + -3y2 + 6 = y

Reorder the terms:
6 + 4y + -3y2 = y

Solving
6 + 4y + -3y2 = y

Solving for variable 'y'.

Reorder the terms:
6 + 4y + -1y + -3y2 = y + -1y

Combine like terms: 4y + -1y = 3y
6 + 3y + -3y2 = y + -1y

Combine like terms: y + -1y = 0
6 + 3y + -3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + y + -1y2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {2, -1}