7v^2-42=35v

Solution for 7v^2-42=35v equation:

Simplifying
7v2 + -42 = 35v

Reorder the terms:
-42 + 7v2 = 35v

Solving
-42 + 7v2 = 35v

Solving for variable 'v'.

Reorder the terms:
-42 + -35v + 7v2 = 35v + -35v

Combine like terms: 35v + -35v = 0
-42 + -35v + 7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -5v + v2) = 0

Factor a trinomial.
7((-1 + -1v)(6 + -1v)) = 0

Ignore the factor 7.
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 '(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 = {-1, 6}