4j^2+6j-4=0

Solution for 4j^2+6j-4=0 equation:

Simplifying
4j2 + 6j + -4 = 0

Reorder the terms:
-4 + 6j + 4j2 = 0

Solving
-4 + 6j + 4j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 3j + 2j2) = 0

Factor a trinomial.
2((-2 + -1j)(1 + -2j)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -2j)' equal to zero and attempt to solve:

Simplifying
1 + -2j = 0

Solving
1 + -2j = 0

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

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

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

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

Divide each side by '-2'.
j = 0.5

Simplifying
j = 0.5
Solution
j = {-2, 0.5}