7v^2-70v+141=-6

Solution for 7v^2-70v+141=-6 equation:

Simplifying
7v2 + -70v + 141 = -6

Reorder the terms:
141 + -70v + 7v2 = -6

Solving
141 + -70v + 7v2 = -6

Solving for variable 'v'.

Reorder the terms:
141 + 6 + -70v + 7v2 = -6 + 6

Combine like terms: 141 + 6 = 147
147 + -70v + 7v2 = -6 + 6

Combine like terms: -6 + 6 = 0
147 + -70v + 7v2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(21 + -10v + v2) = 0

Factor a trinomial.
7((3 + -1v)(7 + -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 '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7
Solution
v = {3, 7}