j^2+4j-21=0

Solution for j^2+4j-21=0 equation:

Simplifying
j2 + 4j + -21 = 0

Reorder the terms:
-21 + 4j + j2 = 0

Solving
-21 + 4j + j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-7 + -1j)(3 + -1j) = 0

Subproblem 1
Set the factor '(-7 + -1j)' equal to zero and attempt to solve:

Simplifying
-7 + -1j = 0

Solving
-7 + -1j = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1j = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1j = 0 + 7
-1j = 0 + 7

Combine like terms: 0 + 7 = 7
-1j = 7

Divide each side by '-1'.
j = -7

Simplifying
j = -7
Subproblem 2
Set the factor '(3 + -1j)' equal to zero and attempt to solve:

Simplifying
3 + -1j = 0

Solving
3 + -1j = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1j = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j = 0 + -3
-1j = 0 + -3

Combine like terms: 0 + -3 = -3
-1j = -3

Divide each side by '-1'.
j = 3

Simplifying
j = 3
Solution
j = {-7, 3}