j(j+1)=29-j+(j+1)

Solution for j(j+1)=29-j+(j+1) equation:

Simplifying
j(j + 1) = 29 + -1j + (j + 1)

Reorder the terms:
j(1 + j) = 29 + -1j + (j + 1)
(1 * j + j * j) = 29 + -1j + (j + 1)
(1j + j2) = 29 + -1j + (j + 1)

Reorder the terms:
1j + j2 = 29 + -1j + (1 + j)

Remove parenthesis around (1 + j)
1j + j2 = 29 + -1j + 1 + j

Reorder the terms:
1j + j2 = 29 + 1 + -1j + j

Combine like terms: 29 + 1 = 30
1j + j2 = 30 + -1j + j

Combine like terms: -1j + j = 0
1j + j2 = 30 + 0
1j + j2 = 30

Solving
1j + j2 = 30

Solving for variable 'j'.

Reorder the terms:
-30 + 1j + j2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 1j + j2 = 0

Factor a trinomial.
(-6 + -1j)(5 + -1j) = 0

Subproblem 1
Set the factor '(-6 + -1j)' equal to zero and attempt to solve:

Simplifying
-6 + -1j = 0

Solving
-6 + -1j = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1j = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1j = 0 + 6
-1j = 0 + 6

Combine like terms: 0 + 6 = 6
-1j = 6

Divide each side by '-1'.
j = -6

Simplifying
j = -6
Subproblem 2
Set the factor '(5 + -1j)' equal to zero and attempt to solve:

Simplifying
5 + -1j = 0

Solving
5 + -1j = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1j = 0 + -5

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

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

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

Simplifying
j = 5
Solution
j = {-6, 5}