(8-4i)(-2+3i)=

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Solution for (8-4i)(-2+3i)= equation: 


Simplifying
(8 + -4i)(-2 + 3i) = 0

Multiply (8 + -4i) * (-2 + 3i)
(8(-2 + 3i) + -4i * (-2 + 3i)) = 0
((-2 * 8 + 3i * 8) + -4i * (-2 + 3i)) = 0
((-16 + 24i) + -4i * (-2 + 3i)) = 0
(-16 + 24i + (-2 * -4i + 3i * -4i)) = 0
(-16 + 24i + (8i + -12i2)) = 0

Combine like terms: 24i + 8i = 32i
(-16 + 32i + -12i2) = 0

Solving
-16 + 32i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 8i + -3i2) = 0

Factor a trinomial.
4((-2 + i)(2 + -3i)) = 0

Ignore the factor 4.

Subproblem 1
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

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
Solution
i = {2, 0.6666666667}

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