(-3i)(-7-5i)(10-8i)=

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Solution for (-3i)(-7-5i)(10-8i)= equation: 


Simplifying
(-3i)(-7 + -5i)(10 + -8i) = 0

Remove parenthesis around (-3i)
-3i(-7 + -5i)(10 + -8i) = 0

Multiply (-7 + -5i) * (10 + -8i)
-3i(-7(10 + -8i) + -5i * (10 + -8i)) = 0
-3i((10 * -7 + -8i * -7) + -5i * (10 + -8i)) = 0
-3i((-70 + 56i) + -5i * (10 + -8i)) = 0
-3i(-70 + 56i + (10 * -5i + -8i * -5i)) = 0
-3i(-70 + 56i + (-50i + 40i2)) = 0

Combine like terms: 56i + -50i = 6i
-3i(-70 + 6i + 40i2) = 0
(-70 * -3i + 6i * -3i + 40i2 * -3i) = 0
(210i + -18i2 + -120i3) = 0

Solving
210i + -18i2 + -120i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6i'.
6i(35 + -3i + -20i2) = 0

Factor a trinomial.
6i((5 + -4i)(7 + 5i)) = 0

Ignore the factor 6.

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

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0

Subproblem 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25

Subproblem 3
Set the factor '(7 + 5i)' equal to zero and attempt to solve:

Simplifying
7 + 5i = 0

Solving
7 + 5i = 0

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

Add '-7' to each side of the equation.
7 + -7 + 5i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5i = 0 + -7
5i = 0 + -7

Combine like terms: 0 + -7 = -7
5i = -7

Divide each side by '5'.
i = -1.4

Simplifying
i = -1.4
Solution
i = {0, 1.25, -1.4}

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