y^2+3y=12y-8

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Solution for y^2+3y=12y-8 equation: 


Simplifying
y2 + 3y = 12y + -8

Reorder the terms:
3y + y2 = 12y + -8

Reorder the terms:
3y + y2 = -8 + 12y

Solving
3y + y2 = -8 + 12y

Solving for variable 'y'.

Reorder the terms:
8 + 3y + -12y + y2 = -8 + 12y + 8 + -12y

Combine like terms: 3y + -12y = -9y
8 + -9y + y2 = -8 + 12y + 8 + -12y

Reorder the terms:
8 + -9y + y2 = -8 + 8 + 12y + -12y

Combine like terms: -8 + 8 = 0
8 + -9y + y2 = 0 + 12y + -12y
8 + -9y + y2 = 12y + -12y

Combine like terms: 12y + -12y = 0
8 + -9y + y2 = 0

Factor a trinomial.
(1 + -1y)(8 + -1y) = 0


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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

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

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

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {1, 8}

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