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((-6 + -1v)(1 + -1v)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
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
Solution
v = {-6, 1}