(4j+1)(4j-4)=

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

Simplifying
(4j + 1)(4j + -4) = 0

Reorder the terms:
(1 + 4j)(4j + -4) = 0

Reorder the terms:
(1 + 4j)(-4 + 4j) = 0

Multiply (1 + 4j) * (-4 + 4j)
(1(-4 + 4j) + 4j * (-4 + 4j)) = 0
((-4 * 1 + 4j * 1) + 4j * (-4 + 4j)) = 0
((-4 + 4j) + 4j * (-4 + 4j)) = 0
(-4 + 4j + (-4 * 4j + 4j * 4j)) = 0
(-4 + 4j + (-16j + 16j2)) = 0

Combine like terms: 4j + -16j = -12j
(-4 + -12j + 16j2) = 0

Solving
-4 + -12j + 16j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -3j + 4j2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -4j)' equal to zero and attempt to solve:

Simplifying
-1 + -4j = 0

Solving
-1 + -4j = 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 + -4j = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4j = 0 + 1
-4j = 0 + 1

Combine like terms: 0 + 1 = 1
-4j = 1

Divide each side by '-4'.
j = -0.25

Simplifying
j = -0.25
Subproblem 2
Set the factor '(1 + -1j)' equal to zero and attempt to solve:

Simplifying
1 + -1j = 0

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

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

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

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

Simplifying
j = 1
Solution
j = {-0.25, 1}