y^2-y+6=-4y+4

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

Simplifying
y2 + -1y + 6 = -4y + 4

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

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

Solving
6 + -1y + y2 = 4 + -4y

Solving for variable 'y'.

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

Combine like terms: 6 + -4 = 2
2 + -1y + 4y + y2 = 4 + -4y + -4 + 4y

Combine like terms: -1y + 4y = 3y
2 + 3y + y2 = 4 + -4y + -4 + 4y

Reorder the terms:
2 + 3y + y2 = 4 + -4 + -4y + 4y

Combine like terms: 4 + -4 = 0
2 + 3y + y2 = 0 + -4y + 4y
2 + 3y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
2 + 3y + y2 = 0

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

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

Simplifying
2 + y = 0

Solving
2 + y = 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 + y = 0 + -2

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

Combine like terms: 0 + -2 = -2
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}