y^2+3y=8+y

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Solution for y^2+3y=8+y equation: 


Simplifying
y2 + 3y = 8 + y

Reorder the terms:
3y + y2 = 8 + y

Solving
3y + y2 = 8 + y

Solving for variable 'y'.

Reorder the terms:
-8 + 3y + -1y + y2 = 8 + y + -8 + -1y

Combine like terms: 3y + -1y = 2y
-8 + 2y + y2 = 8 + y + -8 + -1y

Reorder the terms:
-8 + 2y + y2 = 8 + -8 + y + -1y

Combine like terms: 8 + -8 = 0
-8 + 2y + y2 = 0 + y + -1y
-8 + 2y + y2 = y + -1y

Combine like terms: y + -1y = 0
-8 + 2y + y2 = 0

Factor a trinomial.
(-4 + -1y)(2 + -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 '(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 = {-4, 2}

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