3v^2=-7v+6

Solution for 3v^2=-7v+6 equation:

Simplifying
3v2 = -7v + 6

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

Solving
3v2 = 6 + -7v

Solving for variable 'v'.

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

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

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

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

Factor a trinomial.
(-3 + -1v)(2 + -3v) = 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 '(2 + -3v)' equal to zero and attempt to solve:

Simplifying
2 + -3v = 0

Solving
2 + -3v = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3v = 0 + -2
-3v = 0 + -2

Combine like terms: 0 + -2 = -2
-3v = -2

Divide each side by '-3'.
v = 0.6666666667

Simplifying
v = 0.6666666667
Solution
v = {-3, 0.6666666667}