v^2-2v-43=5

Solution for v^2-2v-43=5 equation:

Simplifying
v2 + -2v + -43 = 5

Reorder the terms:
-43 + -2v + v2 = 5

Solving
-43 + -2v + v2 = 5

Solving for variable 'v'.

Reorder the terms:
-43 + -5 + -2v + v2 = 5 + -5

Combine like terms: -43 + -5 = -48
-48 + -2v + v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-48 + -2v + v2 = 0

Factor a trinomial.
(-6 + -1v)(8 + -1v) = 0

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 '(8 + -1v)' equal to zero and attempt to solve:

Simplifying
8 + -1v = 0

Solving
8 + -1v = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1v = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1v = 0 + -8
-1v = 0 + -8

Combine like terms: 0 + -8 = -8
-1v = -8

Divide each side by '-1'.
v = 8

Simplifying
v = 8
Solution
v = {-6, 8}