y^2-5y-8=-4y+4

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Solution for y^2-5y-8=-4y+4 equation: 


Simplifying
y2 + -5y + -8 = -4y + 4

Reorder the terms:
-8 + -5y + y2 = -4y + 4

Reorder the terms:
-8 + -5y + y2 = 4 + -4y

Solving
-8 + -5y + y2 = 4 + -4y

Solving for variable 'y'.

Reorder the terms:
-8 + -4 + -5y + 4y + y2 = 4 + -4y + -4 + 4y

Combine like terms: -8 + -4 = -12
-12 + -5y + 4y + y2 = 4 + -4y + -4 + 4y

Combine like terms: -5y + 4y = -1y
-12 + -1y + y2 = 4 + -4y + -4 + 4y

Reorder the terms:
-12 + -1y + y2 = 4 + -4 + -4y + 4y

Combine like terms: 4 + -4 = 0
-12 + -1y + y2 = 0 + -4y + 4y
-12 + -1y + y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-12 + -1y + y2 = 0

Factor a trinomial.
(-3 + -1y)(4 + -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 '(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
Solution
y = {-3, 4}

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