v^2-2v-43=-8

Solution for v^2-2v-43=-8 equation:

Simplifying
v2 + -2v + -43 = -8

Reorder the terms:
-43 + -2v + v2 = -8

Solving
-43 + -2v + v2 = -8

Solving for variable 'v'.

Reorder the terms:
-43 + 8 + -2v + v2 = -8 + 8

Combine like terms: -43 + 8 = -35
-35 + -2v + v2 = -8 + 8

Combine like terms: -8 + 8 = 0
-35 + -2v + v2 = 0

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

Subproblem 1
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
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 = {-5, 7}