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

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


Simplifying
-2v2 + -1v + 12 = -3v2 + 6v

Reorder the terms:
12 + -1v + -2v2 = -3v2 + 6v

Reorder the terms:
12 + -1v + -2v2 = 6v + -3v2

Solving
12 + -1v + -2v2 = 6v + -3v2

Solving for variable 'v'.

Reorder the terms:
12 + -1v + -6v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2

Combine like terms: -1v + -6v = -7v
12 + -7v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2

Combine like terms: -2v2 + 3v2 = 1v2
12 + -7v + 1v2 = 6v + -3v2 + -6v + 3v2

Reorder the terms:
12 + -7v + 1v2 = 6v + -6v + -3v2 + 3v2

Combine like terms: 6v + -6v = 0
12 + -7v + 1v2 = 0 + -3v2 + 3v2
12 + -7v + 1v2 = -3v2 + 3v2

Combine like terms: -3v2 + 3v2 = 0
12 + -7v + 1v2 = 0

Factor a trinomial.
(3 + -1v)(4 + -1v) = 0


Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1v = 0 + -3
-1v = 0 + -3

Combine like terms: 0 + -3 = -3
-1v = -3

Divide each side by '-1'.
v = 3

Simplifying
v = 3

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {3, 4}

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