21v^2+3v-18=0

Solution for 21v^2+3v-18=0 equation:

Simplifying
21v2 + 3v + -18 = 0

Reorder the terms:
-18 + 3v + 21v2 = 0

Solving
-18 + 3v + 21v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + v + 7v2) = 0

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

Ignore the factor 3.
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 '(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
Solution
v = {-1, 0.8571428571}