(a+6)(a+7)=90

Solution for (a+6)(a+7)=90 equation:

Simplifying
(a + 6)(a + 7) = 90

Reorder the terms:
(6 + a)(a + 7) = 90

Reorder the terms:
(6 + a)(7 + a) = 90

Multiply (6 + a) * (7 + a)
(6(7 + a) + a(7 + a)) = 90
((7 * 6 + a * 6) + a(7 + a)) = 90
((42 + 6a) + a(7 + a)) = 90
(42 + 6a + (7 * a + a * a)) = 90
(42 + 6a + (7a + a2)) = 90

Combine like terms: 6a + 7a = 13a
(42 + 13a + a2) = 90

Solving
42 + 13a + a2 = 90

Solving for variable 'a'.

Reorder the terms:
42 + -90 + 13a + a2 = 90 + -90

Combine like terms: 42 + -90 = -48
-48 + 13a + a2 = 90 + -90

Combine like terms: 90 + -90 = 0
-48 + 13a + a2 = 0

Factor a trinomial.
(-16 + -1a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-16 + -1a)' equal to zero and attempt to solve:

Simplifying
-16 + -1a = 0

Solving
-16 + -1a = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1a = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1a = 0 + 16
-1a = 0 + 16

Combine like terms: 0 + 16 = 16
-1a = 16

Divide each side by '-1'.
a = -16

Simplifying
a = -16
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 = {-16, 3}