(18-3i)(-7+8i)=0

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Solution for (18-3i)(-7+8i)=0 equation: 


Simplifying
(18 + -3i)(-7 + 8i) = 0

Multiply (18 + -3i) * (-7 + 8i)
(18(-7 + 8i) + -3i * (-7 + 8i)) = 0
((-7 * 18 + 8i * 18) + -3i * (-7 + 8i)) = 0
((-126 + 144i) + -3i * (-7 + 8i)) = 0
(-126 + 144i + (-7 * -3i + 8i * -3i)) = 0
(-126 + 144i + (21i + -24i2)) = 0

Combine like terms: 144i + 21i = 165i
(-126 + 165i + -24i2) = 0

Solving
-126 + 165i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + 55i + -8i2) = 0

Factor a trinomial.
3((-6 + i)(7 + -8i)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-6 + i)' equal to zero and attempt to solve:

Simplifying
-6 + i = 0

Solving
-6 + i = 0

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

Add '6' to each side of the equation.
-6 + 6 + i = 0 + 6

Combine like terms: -6 + 6 = 0
0 + i = 0 + 6
i = 0 + 6

Combine like terms: 0 + 6 = 6
i = 6

Simplifying
i = 6

Subproblem 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve:

Simplifying
7 + -8i = 0

Solving
7 + -8i = 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 + -8i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8i = 0 + -7
-8i = 0 + -7

Combine like terms: 0 + -7 = -7
-8i = -7

Divide each side by '-8'.
i = 0.875

Simplifying
i = 0.875
Solution
i = {6, 0.875}

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