4i(2-3i)(7+3i)=0

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Solution for 4i(2-3i)(7+3i)=0 equation: 


Simplifying
4i(2 + -3i)(7 + 3i) = 0

Multiply (2 + -3i) * (7 + 3i)
4i(2(7 + 3i) + -3i * (7 + 3i)) = 0
4i((7 * 2 + 3i * 2) + -3i * (7 + 3i)) = 0
4i((14 + 6i) + -3i * (7 + 3i)) = 0
4i(14 + 6i + (7 * -3i + 3i * -3i)) = 0
4i(14 + 6i + (-21i + -9i2)) = 0

Combine like terms: 6i + -21i = -15i
4i(14 + -15i + -9i2) = 0
(14 * 4i + -15i * 4i + -9i2 * 4i) = 0
(56i + -60i2 + -36i3) = 0

Solving
56i + -60i2 + -36i3 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4i'.
4i(14 + -15i + -9i2) = 0

Factor a trinomial.
4i((2 + -3i)(7 + 3i)) = 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 '(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 '(7 + 3i)' equal to zero and attempt to solve:

Simplifying
7 + 3i = 0

Solving
7 + 3i = 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 + 3i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3i = 0 + -7
3i = 0 + -7

Combine like terms: 0 + -7 = -7
3i = -7

Divide each side by '3'.
i = -2.333333333

Simplifying
i = -2.333333333
Solution
i = {0, 0.6666666667, -2.333333333}

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