(a+5)(a+2)=54

Solution for (a+5)(a+2)=54 equation:

Simplifying
(a + 5)(a + 2) = 54

Reorder the terms:
(5 + a)(a + 2) = 54

Reorder the terms:
(5 + a)(2 + a) = 54

Multiply (5 + a) * (2 + a)
(5(2 + a) + a(2 + a)) = 54
((2 * 5 + a * 5) + a(2 + a)) = 54
((10 + 5a) + a(2 + a)) = 54
(10 + 5a + (2 * a + a * a)) = 54
(10 + 5a + (2a + a2)) = 54

Combine like terms: 5a + 2a = 7a
(10 + 7a + a2) = 54

Solving
10 + 7a + a2 = 54

Solving for variable 'a'.

Reorder the terms:
10 + -54 + 7a + a2 = 54 + -54

Combine like terms: 10 + -54 = -44
-44 + 7a + a2 = 54 + -54

Combine like terms: 54 + -54 = 0
-44 + 7a + a2 = 0

Factor a trinomial.
(-11 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

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

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

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

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

Simplifying
a = 4
Solution
a = {-11, 4}