7v^2=56v-105

Solution for 7v^2=56v-105 equation:

Simplifying
7v2 = 56v + -105

Reorder the terms:
7v2 = -105 + 56v

Solving
7v2 = -105 + 56v

Solving for variable 'v'.

Reorder the terms:
105 + -56v + 7v2 = -105 + 56v + 105 + -56v

Reorder the terms:
105 + -56v + 7v2 = -105 + 105 + 56v + -56v

Combine like terms: -105 + 105 = 0
105 + -56v + 7v2 = 0 + 56v + -56v
105 + -56v + 7v2 = 56v + -56v

Combine like terms: 56v + -56v = 0
105 + -56v + 7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(15 + -8v + v2) = 0

Factor a trinomial.
7((3 + -1v)(5 + -1v)) = 0

Ignore the factor 7.
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 '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 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 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {3, 5}