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

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

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

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

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

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

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

Solving
15 + 8x + x2 = 63

Solving for variable 'x'.

Reorder the terms:
15 + -63 + 8x + x2 = 63 + -63

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

Combine like terms: 63 + -63 = 0
-48 + 8x + x2 = 0

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

Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve:

Simplifying
-12 + -1x = 0

Solving
-12 + -1x = 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 + -1x = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1x = 0 + 12
-1x = 0 + 12

Combine like terms: 0 + 12 = 12
-1x = 12

Divide each side by '-1'.
x = -12

Simplifying
x = -12
Subproblem 2
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
Solution
x = {-12, 4}