6v^2-3=7v

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

Simplifying
6v2 + -3 = 7v

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

Solving
-3 + 6v2 = 7v

Solving for variable 'v'.

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

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

Factor a trinomial.
(-1 + -3v)(3 + -2v) = 0

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

Simplifying
-1 + -3v = 0

Solving
-1 + -3v = 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 + -3v = 0 + 1

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

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

Divide each side by '-3'.
v = -0.3333333333

Simplifying
v = -0.3333333333
Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve:

Simplifying
3 + -2v = 0

Solving
3 + -2v = 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 + -2v = 0 + -3

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

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

Divide each side by '-2'.
v = 1.5

Simplifying
v = 1.5
Solution
v = {-0.3333333333, 1.5}