a(a+17)=(-60)

Solution for a(a+17)=(-60) equation:

Simplifying
a(a + 17) = (-60)

Reorder the terms:
a(17 + a) = (-60)
(17 * a + a * a) = (-60)
(17a + a2) = (-60)
17a + a2 = -60

Solving
17a + a2 = -60

Solving for variable 'a'.

Reorder the terms:
60 + 17a + a2 = -60 + 60

Combine like terms: -60 + 60 = 0
60 + 17a + a2 = 0

Factor a trinomial.
(12 + a)(5 + a) = 0

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

Simplifying
12 + a = 0

Solving
12 + a = 0

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

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

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

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

Simplifying
a = -12
Subproblem 2
Set the factor '(5 + a)' equal to zero and attempt to solve:

Simplifying
5 + a = 0

Solving
5 + a = 0

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

Add '-5' to each side of the equation.
5 + -5 + a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + a = 0 + -5
a = 0 + -5

Combine like terms: 0 + -5 = -5
a = -5

Simplifying
a = -5
Solution
a = {-12, -5}