40=v(v-3)

Solution for 40=v(v-3) equation:

Simplifying
40 = v(v + -3)

Reorder the terms:
40 = v(-3 + v)
40 = (-3 * v + v * v)
40 = (-3v + v2)

Solving
40 = -3v + v2

Solving for variable 'v'.

Reorder the terms:
40 + 3v + -1v2 = -3v + 3v + v2 + -1v2

Combine like terms: -3v + 3v = 0
40 + 3v + -1v2 = 0 + v2 + -1v2
40 + 3v + -1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
40 + 3v + -1v2 = 0

Factor a trinomial.
(8 + -1v)(5 + v) = 0

Subproblem 1
Set the factor '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v = 0 + -8
-1v = 0 + -8

Combine like terms: 0 + -8 = -8
-1v = -8

Divide each side by '-1'.
v = 8

Simplifying
v = 8
Subproblem 2
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

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

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5
Solution
v = {8, -5}