-2y^2-y+12=-3y^2+6y

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Solution for -2y^2-y+12=-3y^2+6y equation: 


Simplifying
-2y2 + -1y + 12 = -3y2 + 6y

Reorder the terms:
12 + -1y + -2y2 = -3y2 + 6y

Reorder the terms:
12 + -1y + -2y2 = 6y + -3y2

Solving
12 + -1y + -2y2 = 6y + -3y2

Solving for variable 'y'.

Reorder the terms:
12 + -1y + -6y + -2y2 + 3y2 = 6y + -3y2 + -6y + 3y2

Combine like terms: -1y + -6y = -7y
12 + -7y + -2y2 + 3y2 = 6y + -3y2 + -6y + 3y2

Combine like terms: -2y2 + 3y2 = 1y2
12 + -7y + 1y2 = 6y + -3y2 + -6y + 3y2

Reorder the terms:
12 + -7y + 1y2 = 6y + -6y + -3y2 + 3y2

Combine like terms: 6y + -6y = 0
12 + -7y + 1y2 = 0 + -3y2 + 3y2
12 + -7y + 1y2 = -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
12 + -7y + 1y2 = 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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