42j^2-19j-1=0

Solution for 42j^2-19j-1=0 equation:

Simplifying
42j2 + -19j + -1 = 0

Reorder the terms:
-1 + -19j + 42j2 = 0

Solving
-1 + -19j + 42j2 = 0

Solving for variable 'j'.

Factor a trinomial.
(-1 + -21j)(1 + -2j) = 0

Subproblem 1
Set the factor '(-1 + -21j)' equal to zero and attempt to solve:

Simplifying
-1 + -21j = 0

Solving
-1 + -21j = 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 + -21j = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -21j = 0 + 1
-21j = 0 + 1

Combine like terms: 0 + 1 = 1
-21j = 1

Divide each side by '-21'.
j = -0.04761904762

Simplifying
j = -0.04761904762
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 = {-0.04761904762, 0.5}