12=7v-v^2

Solution for 12=7v-v^2 equation:

Simplifying
12 = 7v + -1v2

Solving
12 = 7v + -1v2

Solving for variable 'v'.

Reorder the terms:
12 + -7v + v2 = 7v + -7v + -1v2 + v2

Combine like terms: 7v + -7v = 0
12 + -7v + v2 = 0 + -1v2 + v2
12 + -7v + v2 = -1v2 + v2

Combine like terms: -1v2 + v2 = 0
12 + -7v + v2 = 0

Factor a trinomial.
(3 + -1v)(4 + -1v) = 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 '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

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

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

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {3, 4}