j^2+17j=-72

Solution for j^2+17j=-72 equation:

Simplifying
j2 + 17j = -72

Reorder the terms:
17j + j2 = -72

Solving
17j + j2 = -72

Solving for variable 'j'.

Reorder the terms:
72 + 17j + j2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + 17j + j2 = 0

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

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

Simplifying
9 + j = 0

Solving
9 + j = 0

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

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

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

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

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

Simplifying
8 + j = 0

Solving
8 + j = 0

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

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

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

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

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