7i(8-12i)(8+12i)=1456i

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Solution for 7i(8-12i)(8+12i)=1456i equation: 


Simplifying
7i(8 + -12i)(8 + 12i) = 1456i

Multiply (8 + -12i) * (8 + 12i)
7i(8(8 + 12i) + -12i * (8 + 12i)) = 1456i
7i((8 * 8 + 12i * 8) + -12i * (8 + 12i)) = 1456i
7i((64 + 96i) + -12i * (8 + 12i)) = 1456i
7i(64 + 96i + (8 * -12i + 12i * -12i)) = 1456i
7i(64 + 96i + (-96i + -144i2)) = 1456i

Combine like terms: 96i + -96i = 0
7i(64 + 0 + -144i2) = 1456i
7i(64 + -144i2) = 1456i
(64 * 7i + -144i2 * 7i) = 1456i
(448i + -1008i3) = 1456i

Solving
448i + -1008i3 = 1456i

Solving for variable 'i'.

Reorder the terms:
448i + -1456i + -1008i3 = 1456i + -1456i

Combine like terms: 448i + -1456i = -1008i
-1008i + -1008i3 = 1456i + -1456i

Combine like terms: 1456i + -1456i = 0
-1008i + -1008i3 = 0

Factor out the Greatest Common Factor (GCF), '-1008i'.
-1008i(1 + i2) = 0

Ignore the factor -1008.

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 + i2)' equal to zero and attempt to solve:

Simplifying
1 + i2 = 0

Solving
1 + i2 = 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 + i2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + i2 = 0 + -1
i2 = 0 + -1

Combine like terms: 0 + -1 = -1
i2 = -1

Simplifying
i2 = -1

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
i = {0}

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