3y+2=y^2-4y-28

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Solution for 3y+2=y^2-4y-28 equation: 


Simplifying
3y + 2 = y2 + -4y + -28

Reorder the terms:
2 + 3y = y2 + -4y + -28

Reorder the terms:
2 + 3y = -28 + -4y + y2

Solving
2 + 3y = -28 + -4y + y2

Solving for variable 'y'.

Reorder the terms:
2 + 28 + 3y + 4y + -1y2 = -28 + -4y + y2 + 28 + 4y + -1y2

Combine like terms: 2 + 28 = 30
30 + 3y + 4y + -1y2 = -28 + -4y + y2 + 28 + 4y + -1y2

Combine like terms: 3y + 4y = 7y
30 + 7y + -1y2 = -28 + -4y + y2 + 28 + 4y + -1y2

Reorder the terms:
30 + 7y + -1y2 = -28 + 28 + -4y + 4y + y2 + -1y2

Combine like terms: -28 + 28 = 0
30 + 7y + -1y2 = 0 + -4y + 4y + y2 + -1y2
30 + 7y + -1y2 = -4y + 4y + y2 + -1y2

Combine like terms: -4y + 4y = 0
30 + 7y + -1y2 = 0 + y2 + -1y2
30 + 7y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
30 + 7y + -1y2 = 0

Factor a trinomial.
(10 + -1y)(3 + y) = 0


Subproblem 1
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10

Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {10, -3}

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