(3i+2j)(7i+9j)=

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Solution for (3i+2j)(7i+9j)= equation: 


Simplifying
(3i + 2j)(7i + 9j) = 0

Multiply (3i + 2j) * (7i + 9j)
(3i * (7i + 9j) + 2j * (7i + 9j)) = 0
((7i * 3i + 9j * 3i) + 2j * (7i + 9j)) = 0

Reorder the terms:
((27ij + 21i2) + 2j * (7i + 9j)) = 0
((27ij + 21i2) + 2j * (7i + 9j)) = 0
(27ij + 21i2 + (7i * 2j + 9j * 2j)) = 0
(27ij + 21i2 + (14ij + 18j2)) = 0

Reorder the terms:
(27ij + 14ij + 21i2 + 18j2) = 0

Combine like terms: 27ij + 14ij = 41ij
(41ij + 21i2 + 18j2) = 0

Solving
41ij + 21i2 + 18j2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3i + 2j)(7i + 9j) = 0


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 '(7i + 9j)' equal to zero and attempt to solve:

Simplifying
7i + 9j = 0

Solving
7i + 9j = 0

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

Add '-9j' to each side of the equation.
7i + 9j + -9j = 0 + -9j

Combine like terms: 9j + -9j = 0
7i + 0 = 0 + -9j
7i = 0 + -9j
Remove the zero:
7i = -9j

Divide each side by '7'.
i = -1.285714286j

Simplifying
i = -1.285714286j
Solution
i = {-0.6666666667j, -1.285714286j}

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