4j(4-7j)=1

Solution for 4j(4-7j)=1 equation:

Simplifying
4j(4 + -7j) = 1
(4 * 4j + -7j * 4j) = 1
(16j + -28j2) = 1

Solving
16j + -28j2 = 1

Solving for variable 'j'.

Reorder the terms:
-1 + 16j + -28j2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 16j + -28j2 = 0

Factor a trinomial.
(-1 + 2j)(1 + -14j) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -14j)' equal to zero and attempt to solve:

Simplifying
1 + -14j = 0

Solving
1 + -14j = 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 + -14j = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -14j = 0 + -1
-14j = 0 + -1

Combine like terms: 0 + -1 = -1
-14j = -1

Divide each side by '-14'.
j = 0.07142857143

Simplifying
j = 0.07142857143
Solution
j = {0.5, 0.07142857143}