i(4-8i)(7-4i)=

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Solution for i(4-8i)(7-4i)= equation: 


Simplifying
i(4 + -8i)(7 + -4i) = 0

Multiply (4 + -8i) * (7 + -4i)
i(4(7 + -4i) + -8i * (7 + -4i)) = 0
i((7 * 4 + -4i * 4) + -8i * (7 + -4i)) = 0
i((28 + -16i) + -8i * (7 + -4i)) = 0
i(28 + -16i + (7 * -8i + -4i * -8i)) = 0
i(28 + -16i + (-56i + 32i2)) = 0

Combine like terms: -16i + -56i = -72i
i(28 + -72i + 32i2) = 0
(28 * i + -72i * i + 32i2 * i) = 0
(28i + -72i2 + 32i3) = 0

Solving
28i + -72i2 + 32i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4i'.
4i(7 + -18i + 8i2) = 0

Factor a trinomial.
4i((1 + -2i)(7 + -4i)) = 0

Ignore the factor 4.

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 '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5

Subproblem 3
Set the factor '(7 + -4i)' equal to zero and attempt to solve:

Simplifying
7 + -4i = 0

Solving
7 + -4i = 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 + -4i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4i = 0 + -7
-4i = 0 + -7

Combine like terms: 0 + -7 = -7
-4i = -7

Divide each side by '-4'.
i = 1.75

Simplifying
i = 1.75
Solution
i = {0, 0.5, 1.75}

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