4(6i-8j)(-2i-10j)=

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Solution for 4(6i-8j)(-2i-10j)= equation: 


Simplifying
4(6i + -8j)(-2i + -10j) = 0

Multiply (6i + -8j) * (-2i + -10j)
4(6i * (-2i + -10j) + -8j * (-2i + -10j)) = 0
4((-2i * 6i + -10j * 6i) + -8j * (-2i + -10j)) = 0

Reorder the terms:
4((-60ij + -12i2) + -8j * (-2i + -10j)) = 0
4((-60ij + -12i2) + -8j * (-2i + -10j)) = 0
4(-60ij + -12i2 + (-2i * -8j + -10j * -8j)) = 0
4(-60ij + -12i2 + (16ij + 80j2)) = 0

Reorder the terms:
4(-60ij + 16ij + -12i2 + 80j2) = 0

Combine like terms: -60ij + 16ij = -44ij
4(-44ij + -12i2 + 80j2) = 0
(-44ij * 4 + -12i2 * 4 + 80j2 * 4) = 0
(-176ij + -48i2 + 320j2) = 0

Solving
-176ij + -48i2 + 320j2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '16'.
16(-11ij + -3i2 + 20j2) = 0

Factor a trinomial.
16((-1i + -5j)(3i + -4j)) = 0

Ignore the factor 16.

Subproblem 1
Set the factor '(-1i + -5j)' equal to zero and attempt to solve:

Simplifying
-1i + -5j = 0

Solving
-1i + -5j = 0

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

Add '5j' to each side of the equation.
-1i + -5j + 5j = 0 + 5j

Combine like terms: -5j + 5j = 0
-1i + 0 = 0 + 5j
-1i = 0 + 5j
Remove the zero:
-1i = 5j

Divide each side by '-1'.
i = -5j

Simplifying
i = -5j

Subproblem 2
Set the factor '(3i + -4j)' equal to zero and attempt to solve:

Simplifying
3i + -4j = 0

Solving
3i + -4j = 0

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

Add '4j' to each side of the equation.
3i + -4j + 4j = 0 + 4j

Combine like terms: -4j + 4j = 0
3i + 0 = 0 + 4j
3i = 0 + 4j
Remove the zero:
3i = 4j

Divide each side by '3'.
i = 1.333333333j

Simplifying
i = 1.333333333j
Solution
i = {-5j, 1.333333333j}

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