(v+3)(v+1)=63

Solution for (v+3)(v+1)=63 equation:

Simplifying
(v + 3)(v + 1) = 63

Reorder the terms:
(3 + v)(v + 1) = 63

Reorder the terms:
(3 + v)(1 + v) = 63

Multiply (3 + v) * (1 + v)
(3(1 + v) + v(1 + v)) = 63
((1 * 3 + v * 3) + v(1 + v)) = 63
((3 + 3v) + v(1 + v)) = 63
(3 + 3v + (1 * v + v * v)) = 63
(3 + 3v + (1v + v2)) = 63

Combine like terms: 3v + 1v = 4v
(3 + 4v + v2) = 63

Solving
3 + 4v + v2 = 63

Solving for variable 'v'.

Reorder the terms:
3 + -63 + 4v + v2 = 63 + -63

Combine like terms: 3 + -63 = -60
-60 + 4v + v2 = 63 + -63

Combine like terms: 63 + -63 = 0
-60 + 4v + v2 = 0

Factor a trinomial.
(-10 + -1v)(6 + -1v) = 0

Subproblem 1
Set the factor '(-10 + -1v)' equal to zero and attempt to solve:

Simplifying
-10 + -1v = 0

Solving
-10 + -1v = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1v = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1v = 0 + 10
-1v = 0 + 10

Combine like terms: 0 + 10 = 10
-1v = 10

Divide each side by '-1'.
v = -10

Simplifying
v = -10
Subproblem 2
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
Solution
v = {-10, 6}