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

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


Simplifying
(-1i + 4j) * x(3i + 2j) = 0

Reorder the terms for easier multiplication:
x(-1i + 4j)(3i + 2j) = 0

Multiply (-1i + 4j) * (3i + 2j)
x(-1i * (3i + 2j) + 4j * (3i + 2j)) = 0
x((3i * -1i + 2j * -1i) + 4j * (3i + 2j)) = 0

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

Reorder the terms:
x(-2ij + 12ij + -3i2 + 8j2) = 0

Combine like terms: -2ij + 12ij = 10ij
x(10ij + -3i2 + 8j2) = 0
(10ij * x + -3i2 * x + 8j2 * x) = 0
(10ijx + -3i2x + 8j2x) = 0

Solving
10ijx + -3i2x + 8j2x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(10ij + -3i2 + 8j2) = 0

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
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 3
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 = {-0.6666666667j, 4j}

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