7i(8-12i)(8+12i)=0

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Solution for 7i(8-12i)(8+12i)=0 equation: 


Simplifying
7i(8 + -12i)(8 + 12i) = 0

Multiply (8 + -12i) * (8 + 12i)
7i(8(8 + 12i) + -12i * (8 + 12i)) = 0
7i((8 * 8 + 12i * 8) + -12i * (8 + 12i)) = 0
7i((64 + 96i) + -12i * (8 + 12i)) = 0
7i(64 + 96i + (8 * -12i + 12i * -12i)) = 0
7i(64 + 96i + (-96i + -144i2)) = 0

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

Solving
448i + -1008i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '112i'.
112i(4 + -9i2) = 0

Factor a difference between two squares.
112i((2 + 3i)(2 + -3i)) = 0

Ignore the factor 112.

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 '(2 + 3i)' equal to zero and attempt to solve:

Simplifying
2 + 3i = 0

Solving
2 + 3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3i = 0 + -2
3i = 0 + -2

Combine like terms: 0 + -2 = -2
3i = -2

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667

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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
Solution
i = {0, -0.6666666667, 0.6666666667}

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