7v^2-27v+18=0

Solution for 7v^2-27v+18=0 equation:

Simplifying
7v2 + -27v + 18 = 0

Reorder the terms:
18 + -27v + 7v2 = 0

Solving
18 + -27v + 7v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(6 + -7v)(3 + -1v) = 0

Subproblem 1
Set the factor '(6 + -7v)' equal to zero and attempt to solve:

Simplifying
6 + -7v = 0

Solving
6 + -7v = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7v = 0 + -6

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

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

Divide each side by '-7'.
v = 0.8571428571

Simplifying
v = 0.8571428571
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 = {0.8571428571, 3}