(4j+4i)(2j+3i)=

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Solution for (4j+4i)(2j+3i)= equation: 


Simplifying
(4j + 4i)(2j + 3i) = 0

Reorder the terms:
(4i + 4j)(2j + 3i) = 0

Reorder the terms:
(4i + 4j)(3i + 2j) = 0

Multiply (4i + 4j) * (3i + 2j)
(4i * (3i + 2j) + 4j * (3i + 2j)) = 0
((3i * 4i + 2j * 4i) + 4j * (3i + 2j)) = 0

Reorder the terms:
((8ij + 12i2) + 4j * (3i + 2j)) = 0
((8ij + 12i2) + 4j * (3i + 2j)) = 0
(8ij + 12i2 + (3i * 4j + 2j * 4j)) = 0
(8ij + 12i2 + (12ij + 8j2)) = 0

Reorder the terms:
(8ij + 12ij + 12i2 + 8j2) = 0

Combine like terms: 8ij + 12ij = 20ij
(20ij + 12i2 + 8j2) = 0

Solving
20ij + 12i2 + 8j2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(5ij + 3i2 + 2j2) = 0

Factor a trinomial.
4((3i + 2j)(i + j)) = 0

Ignore the factor 4.

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

Simplifying
3i + 2j = 0

Solving
3i + 2j = 0

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

Add '-2j' to each side of the equation.
3i + 2j + -2j = 0 + -2j

Combine like terms: 2j + -2j = 0
3i + 0 = 0 + -2j
3i = 0 + -2j
Remove the zero:
3i = -2j

Divide each side by '3'.
i = -0.6666666667j

Simplifying
i = -0.6666666667j

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

Simplifying
i + j = 0

Solving
i + j = 0

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

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

Combine like terms: j + -1j = 0
i + 0 = 0 + -1j
i = 0 + -1j
Remove the zero:
i = -1j

Simplifying
i = -1j
Solution
i = {-0.6666666667j, -1j}

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