0=4v^2-3v-27

Solution for 0=4v^2-3v-27 equation:

Simplifying
0 = 4v2 + -3v + -27

Reorder the terms:
0 = -27 + -3v + 4v2

Solving
0 = -27 + -3v + 4v2

Solving for variable 'v'.

Combine like terms: 0 + 27 = 27
27 + 3v + -4v2 = -27 + -3v + 4v2 + 27 + 3v + -4v2

Reorder the terms:
27 + 3v + -4v2 = -27 + 27 + -3v + 3v + 4v2 + -4v2

Combine like terms: -27 + 27 = 0
27 + 3v + -4v2 = 0 + -3v + 3v + 4v2 + -4v2
27 + 3v + -4v2 = -3v + 3v + 4v2 + -4v2

Combine like terms: -3v + 3v = 0
27 + 3v + -4v2 = 0 + 4v2 + -4v2
27 + 3v + -4v2 = 4v2 + -4v2

Combine like terms: 4v2 + -4v2 = 0
27 + 3v + -4v2 = 0

Factor a trinomial.
(3 + -1v)(9 + 4v) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + 4v)' equal to zero and attempt to solve:

Simplifying
9 + 4v = 0

Solving
9 + 4v = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4v = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4v = 0 + -9
4v = 0 + -9

Combine like terms: 0 + -9 = -9
4v = -9

Divide each side by '4'.
v = -2.25

Simplifying
v = -2.25
Solution
v = {3, -2.25}