(-9-3i)(2+i)=

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Solution for (-9-3i)(2+i)= equation:


Simplifying
(-9 + -3i)(2 + i) = 0

Multiply (-9 + -3i) * (2 + i)
(-9(2 + i) + -3i * (2 + i)) = 0
((2 * -9 + i * -9) + -3i * (2 + i)) = 0
((-18 + -9i) + -3i * (2 + i)) = 0
(-18 + -9i + (2 * -3i + i * -3i)) = 0
(-18 + -9i + (-6i + -3i2)) = 0

Combine like terms: -9i + -6i = -15i
(-18 + -15i + -3i2) = 0

Solving
-18 + -15i + -3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(6 + 5i + i2) = 0

Factor a trinomial.
-3((3 + i)(2 + i)) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3

Subproblem 2

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

Solution

i = {-3, -2}

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