y^2+y+1=-y+4

Solution for y^2+y+1=-y+4 equation:

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

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

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

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

Solving for variable 'y'.

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

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

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

Reorder the terms:
-3 + 2y + y2 = 4 + -4 + -1y + y

Combine like terms: 4 + -4 = 0
-3 + 2y + y2 = 0 + -1y + y
-3 + 2y + y2 = -1y + y

Combine like terms: -1y + y = 0
-3 + 2y + y2 = 0

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

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

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 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 + -1y = 0 + 3

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

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

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
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
Solution
y = {-3, 1}