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.
(5 + -1a)(12 + -1a) = 0

Subproblem 1
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 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 + -1a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1a = 0 + -5
-1a = 0 + -5

Combine like terms: 0 + -5 = -5
-1a = -5

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Subproblem 2
Set the factor '(12 + -1a)' equal to zero and attempt to solve:

Simplifying
12 + -1a = 0

Solving
12 + -1a = 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 + -1a = 0 + -12

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

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

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

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