(6-3i)(10+2i)=0

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Solution for (6-3i)(10+2i)=0 equation:


Simplifying
(6 + -3i)(10 + 2i) = 0

Multiply (6 + -3i) * (10 + 2i)
(6(10 + 2i) + -3i * (10 + 2i)) = 0
((10 * 6 + 2i * 6) + -3i * (10 + 2i)) = 0
((60 + 12i) + -3i * (10 + 2i)) = 0
(60 + 12i + (10 * -3i + 2i * -3i)) = 0
(60 + 12i + (-30i + -6i2)) = 0

Combine like terms: 12i + -30i = -18i
(60 + -18i + -6i2) = 0

Solving
60 + -18i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + -3i + -1i2) = 0

Factor a trinomial.
6((2 + -1i)(5 + i)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2

Subproblem 2

Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5

Solution

i = {2, -5}

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