-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 = -5v2
12 + -7v + -5v2 = 6v + 3v2 + -6v + -3v2

Reorder the terms:
12 + -7v + -5v2 = 6v + -6v + 3v2 + -3v2

Combine like terms: 6v + -6v = 0
12 + -7v + -5v2 = 0 + 3v2 + -3v2
12 + -7v + -5v2 = 3v2 + -3v2

Combine like terms: 3v2 + -3v2 = 0
12 + -7v + -5v2 = 0

Factor a trinomial.
(1 + -1v)(12 + 5v) = 0


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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 0

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

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

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

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

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

Simplifying
v = 1

Subproblem 2
Set the factor '(12 + 5v)' equal to zero and attempt to solve:

Simplifying
12 + 5v = 0

Solving
12 + 5v = 0

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

Add '-12' to each side of the equation.
12 + -12 + 5v = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5v = 0 + -12
5v = 0 + -12

Combine like terms: 0 + -12 = -12
5v = -12

Divide each side by '5'.
v = -2.4

Simplifying
v = -2.4
Solution
v = {1, -2.4}

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