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

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Solution for 4(3i+j)(i+4j)=0 equation: 


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

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

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

Reorder the terms:
4(12ij + ij + 3i2 + 4j2) = 0

Combine like terms: 12ij + ij = 13ij
4(13ij + 3i2 + 4j2) = 0
(13ij * 4 + 3i2 * 4 + 4j2 * 4) = 0
(52ij + 12i2 + 16j2) = 0

Solving
52ij + 12i2 + 16j2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(13ij + 3i2 + 4j2) = 0

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

Ignore the factor 4.

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

Simplifying
3i + j = 0

Solving
3i + j = 0

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

Add '-1j' to each side of the equation.
3i + j + -1j = 0 + -1j

Combine like terms: j + -1j = 0
3i + 0 = 0 + -1j
3i = 0 + -1j
Remove the zero:
3i = -1j

Divide each side by '3'.
i = -0.3333333333j

Simplifying
i = -0.3333333333j

Subproblem 2
Set the factor '(i + 4j)' equal to zero and attempt to solve:

Simplifying
i + 4j = 0

Solving
i + 4j = 0

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

Add '-4j' to each side of the equation.
i + 4j + -4j = 0 + -4j

Combine like terms: 4j + -4j = 0
i + 0 = 0 + -4j
i = 0 + -4j
Remove the zero:
i = -4j

Simplifying
i = -4j
Solution
i = {-0.3333333333j, -4j}

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