4v(v-3)=11v+6

Solution for 4v(v-3)=11v+6 equation:

Simplifying
4v(v + -3) = 11v + 6

Reorder the terms:
4v(-3 + v) = 11v + 6
(-3 * 4v + v * 4v) = 11v + 6
(-12v + 4v2) = 11v + 6

Reorder the terms:
-12v + 4v2 = 6 + 11v

Solving
-12v + 4v2 = 6 + 11v

Solving for variable 'v'.

Reorder the terms:
-6 + -12v + -11v + 4v2 = 6 + 11v + -6 + -11v

Combine like terms: -12v + -11v = -23v
-6 + -23v + 4v2 = 6 + 11v + -6 + -11v

Reorder the terms:
-6 + -23v + 4v2 = 6 + -6 + 11v + -11v

Combine like terms: 6 + -6 = 0
-6 + -23v + 4v2 = 0 + 11v + -11v
-6 + -23v + 4v2 = 11v + -11v

Combine like terms: 11v + -11v = 0
-6 + -23v + 4v2 = 0

Factor a trinomial.
(-1 + -4v)(6 + -1v) = 0

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

Simplifying
-1 + -4v = 0

Solving
-1 + -4v = 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 + -4v = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4v = 0 + 1
-4v = 0 + 1

Combine like terms: 0 + 1 = 1
-4v = 1

Divide each side by '-4'.
v = -0.25

Simplifying
v = -0.25
Subproblem 2
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 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 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6
Solution
v = {-0.25, 6}