y+4=y^2+3y-4

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Solution for y+4=y^2+3y-4 equation: 


Simplifying
y + 4 = y2 + 3y + -4

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

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

Solving
4 + y = -4 + 3y + y2

Solving for variable 'y'.

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

Combine like terms: 4 + 4 = 8
8 + y + -3y + -1y2 = -4 + 3y + y2 + 4 + -3y + -1y2

Combine like terms: y + -3y = -2y
8 + -2y + -1y2 = -4 + 3y + y2 + 4 + -3y + -1y2

Reorder the terms:
8 + -2y + -1y2 = -4 + 4 + 3y + -3y + y2 + -1y2

Combine like terms: -4 + 4 = 0
8 + -2y + -1y2 = 0 + 3y + -3y + y2 + -1y2
8 + -2y + -1y2 = 3y + -3y + y2 + -1y2

Combine like terms: 3y + -3y = 0
8 + -2y + -1y2 = 0 + y2 + -1y2
8 + -2y + -1y2 = y2 + -1y2

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

Factor a trinomial.
(2 + -1y)(4 + y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + y)' equal to zero and attempt to solve:

Simplifying
4 + y = 0

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

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

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

Simplifying
y = -4
Solution
y = {2, -4}

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