2y^2-y=y+4

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

Simplifying
2y2 + -1y = y + 4

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

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

Solving
-1y + 2y2 = 4 + y

Solving for variable 'y'.

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

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

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

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

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

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
y = {-1, 2}