v(9v+2)=7

Solution for v(9v+2)=7 equation:

Simplifying
v(9v + 2) = 7

Reorder the terms:
v(2 + 9v) = 7
(2 * v + 9v * v) = 7
(2v + 9v2) = 7

Solving
2v + 9v2 = 7

Solving for variable 'v'.

Reorder the terms:
-7 + 2v + 9v2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + 2v + 9v2 = 0

Factor a trinomial.
(-1 + -1v)(7 + -9v) = 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 '(7 + -9v)' equal to zero and attempt to solve:

Simplifying
7 + -9v = 0

Solving
7 + -9v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9v = 0 + -7
-9v = 0 + -7

Combine like terms: 0 + -7 = -7
-9v = -7

Divide each side by '-9'.
v = 0.7777777778

Simplifying
v = 0.7777777778
Solution
v = {-1, 0.7777777778}