7v^2=19v+6

Solution for 7v^2=19v+6 equation:

Simplifying
7v2 = 19v + 6

Reorder the terms:
7v2 = 6 + 19v

Solving
7v2 = 6 + 19v

Solving for variable 'v'.

Reorder the terms:
-6 + -19v + 7v2 = 6 + 19v + -6 + -19v

Reorder the terms:
-6 + -19v + 7v2 = 6 + -6 + 19v + -19v

Combine like terms: 6 + -6 = 0
-6 + -19v + 7v2 = 0 + 19v + -19v
-6 + -19v + 7v2 = 19v + -19v

Combine like terms: 19v + -19v = 0
-6 + -19v + 7v2 = 0

Factor a trinomial.
(-2 + -7v)(3 + -1v) = 0

Subproblem 1
Set the factor '(-2 + -7v)' equal to zero and attempt to solve:

Simplifying
-2 + -7v = 0

Solving
-2 + -7v = 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 + -7v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7v = 0 + 2
-7v = 0 + 2

Combine like terms: 0 + 2 = 2
-7v = 2

Divide each side by '-7'.
v = -0.2857142857

Simplifying
v = -0.2857142857
Subproblem 2
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
Solution
v = {-0.2857142857, 3}