x(x+17)=-72

Solution for x(x+17)=-72 equation:

Simplifying
x(x + 17) = -72

Reorder the terms:
x(17 + x) = -72
(17 * x + x * x) = -72
(17x + x2) = -72

Solving
17x + x2 = -72

Solving for variable 'x'.

Reorder the terms:
72 + 17x + x2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + 17x + x2 = 0

Factor a trinomial.
(9 + x)(8 + x) = 0

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 0

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

Add '-8' to each side of the equation.
8 + -8 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-9, -8}