y^2+5y=4+2y

Solution for y^2+5y=4+2y equation:

Simplifying
y2 + 5y = 4 + 2y

Reorder the terms:
5y + y2 = 4 + 2y

Solving
5y + y2 = 4 + 2y

Solving for variable 'y'.

Reorder the terms:
-4 + 5y + -2y + y2 = 4 + 2y + -4 + -2y

Combine like terms: 5y + -2y = 3y
-4 + 3y + y2 = 4 + 2y + -4 + -2y

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

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

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

Factor a trinomial.
(-4 + -1y)(1 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 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 + -1y = 0 + 4

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

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

Divide each side by '-1'.
y = -4

Simplifying
y = -4
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 = {-4, 1}