v^2-7v=30

Solution for v^2-7v=30 equation:

Simplifying
v2 + -7v = 30

Reorder the terms:
-7v + v2 = 30

Solving
-7v + v2 = 30

Solving for variable 'v'.

Reorder the terms:
-30 + -7v + v2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -7v + v2 = 0

Factor a trinomial.
(-3 + -1v)(10 + -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 '(10 + -1v)' equal to zero and attempt to solve:

Simplifying
10 + -1v = 0

Solving
10 + -1v = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1v = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1v = 0 + -10
-1v = 0 + -10

Combine like terms: 0 + -10 = -10
-1v = -10

Divide each side by '-1'.
v = 10

Simplifying
v = 10
Solution
v = {-3, 10}