j^4-7j^2+12=0

Solution for j^4-7j^2+12=0 equation:

Simplifying
j4 + -7j2 + 12 = 0

Reorder the terms:
12 + -7j2 + j4 = 0

Solving
12 + -7j2 + j4 = 0

Solving for variable 'j'.

Factor a trinomial.
(3 + -1j2)(4 + -1j2) = 0

Factor a difference between two squares.
(3 + -1j2)((2 + j)(2 + -1j)) = 0

Subproblem 1
Set the factor '(3 + -1j2)' equal to zero and attempt to solve:

Simplifying
3 + -1j2 = 0

Solving
3 + -1j2 = 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 + -1j2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1j2 = 0 + -3
-1j2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1j2 = -3

Divide each side by '-1'.
j2 = 3

Simplifying
j2 = 3

Take the square root of each side:
j = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(2 + j)' equal to zero and attempt to solve:

Simplifying
2 + j = 0

Solving
2 + j = 0

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

Add '-2' to each side of the equation.
2 + -2 + j = 0 + -2

Combine like terms: 2 + -2 = 0
0 + j = 0 + -2
j = 0 + -2

Combine like terms: 0 + -2 = -2
j = -2

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

Simplifying
2 + -1j = 0

Solving
2 + -1j = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1j = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1j = 0 + -2
-1j = 0 + -2

Combine like terms: 0 + -2 = -2
-1j = -2

Divide each side by '-1'.
j = 2

Simplifying
j = 2
Solution
j = {-1.732050808, 1.732050808, -2, 2}