(a+4)(a+6)=63

Solution for (a+4)(a+6)=63 equation:

Simplifying
(a + 4)(a + 6) = 63

Reorder the terms:
(4 + a)(a + 6) = 63

Reorder the terms:
(4 + a)(6 + a) = 63

Multiply (4 + a) * (6 + a)
(4(6 + a) + a(6 + a)) = 63
((6 * 4 + a * 4) + a(6 + a)) = 63
((24 + 4a) + a(6 + a)) = 63
(24 + 4a + (6 * a + a * a)) = 63
(24 + 4a + (6a + a2)) = 63

Combine like terms: 4a + 6a = 10a
(24 + 10a + a2) = 63

Solving
24 + 10a + a2 = 63

Solving for variable 'a'.

Reorder the terms:
24 + -63 + 10a + a2 = 63 + -63

Combine like terms: 24 + -63 = -39
-39 + 10a + a2 = 63 + -63

Combine like terms: 63 + -63 = 0
-39 + 10a + a2 = 0

Factor a trinomial.
(-13 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-13 + -1a)' equal to zero and attempt to solve:

Simplifying
-13 + -1a = 0

Solving
-13 + -1a = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1a = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1a = 0 + 13
-1a = 0 + 13

Combine like terms: 0 + 13 = 13
-1a = 13

Divide each side by '-1'.
a = -13

Simplifying
a = -13
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-13, 3}