3v^2-72v-75=0

Solution for 3v^2-72v-75=0 equation:

Simplifying
3v2 + -72v + -75 = 0

Reorder the terms:
-75 + -72v + 3v2 = 0

Solving
-75 + -72v + 3v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + -24v + v2) = 0

Factor a trinomial.
3((-1 + -1v)(25 + -1v)) = 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 '(25 + -1v)' equal to zero and attempt to solve:

Simplifying
25 + -1v = 0

Solving
25 + -1v = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1v = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1v = 0 + -25
-1v = 0 + -25

Combine like terms: 0 + -25 = -25
-1v = -25

Divide each side by '-1'.
v = 25

Simplifying
v = 25
Solution
v = {-1, 25}