63=(x+5)(x+3)

Solution for 63=(x+5)(x+3) equation:

Simplifying
63 = (x + 5)(x + 3)

Reorder the terms:
63 = (5 + x)(x + 3)

Reorder the terms:
63 = (5 + x)(3 + x)

Multiply (5 + x) * (3 + x)
63 = (5(3 + x) + x(3 + x))
63 = ((3 * 5 + x * 5) + x(3 + x))
63 = ((15 + 5x) + x(3 + x))
63 = (15 + 5x + (3 * x + x * x))
63 = (15 + 5x + (3x + x2))

Combine like terms: 5x + 3x = 8x
63 = (15 + 8x + x2)

Solving
63 = 15 + 8x + x2

Solving for variable 'x'.

Combine like terms: 63 + -15 = 48
48 + -8x + -1x2 = 15 + 8x + x2 + -15 + -8x + -1x2

Reorder the terms:
48 + -8x + -1x2 = 15 + -15 + 8x + -8x + x2 + -1x2

Combine like terms: 15 + -15 = 0
48 + -8x + -1x2 = 0 + 8x + -8x + x2 + -1x2
48 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
48 + -8x + -1x2 = 0 + x2 + -1x2
48 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -8x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(12 + x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

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

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

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

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

Simplifying
x = 4
Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve:

Simplifying
12 + x = 0

Solving
12 + x = 0

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

Add '-12' to each side of the equation.
12 + -12 + x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + x = 0 + -12
x = 0 + -12

Combine like terms: 0 + -12 = -12
x = -12

Simplifying
x = -12
Solution
x = {4, -12}