y^2-4y-8=5y+28

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Solution for y^2-4y-8=5y+28 equation: 


Simplifying
y2 + -4y + -8 = 5y + 28

Reorder the terms:
-8 + -4y + y2 = 5y + 28

Reorder the terms:
-8 + -4y + y2 = 28 + 5y

Solving
-8 + -4y + y2 = 28 + 5y

Solving for variable 'y'.

Reorder the terms:
-8 + -28 + -4y + -5y + y2 = 28 + 5y + -28 + -5y

Combine like terms: -8 + -28 = -36
-36 + -4y + -5y + y2 = 28 + 5y + -28 + -5y

Combine like terms: -4y + -5y = -9y
-36 + -9y + y2 = 28 + 5y + -28 + -5y

Reorder the terms:
-36 + -9y + y2 = 28 + -28 + 5y + -5y

Combine like terms: 28 + -28 = 0
-36 + -9y + y2 = 0 + 5y + -5y
-36 + -9y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-36 + -9y + y2 = 0

Factor a trinomial.
(-3 + -1y)(12 + -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 '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

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

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

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Solution
y = {-3, 12}

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