v^2-2v-3=5

Solution for v^2-2v-3=5 equation:

Simplifying
v2 + -2v + -3 = 5

Reorder the terms:
-3 + -2v + v2 = 5

Solving
-3 + -2v + v2 = 5

Solving for variable 'v'.

Reorder the terms:
-3 + -5 + -2v + v2 = 5 + -5

Combine like terms: -3 + -5 = -8
-8 + -2v + v2 = 5 + -5

Combine like terms: 5 + -5 = 0
-8 + -2v + v2 = 0

Factor a trinomial.
(-2 + -1v)(4 + -1v) = 0

Subproblem 1
Set the factor '(-2 + -1v)' equal to zero and attempt to solve:

Simplifying
-2 + -1v = 0

Solving
-2 + -1v = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1v = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1v = 0 + 2
-1v = 0 + 2

Combine like terms: 0 + 2 = 2
-1v = 2

Divide each side by '-1'.
v = -2

Simplifying
v = -2
Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-2, 4}