(4-6i)(5-4i)=

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Solution for (4-6i)(5-4i)= equation: 


Simplifying
(4 + -6i)(5 + -4i) = 0

Multiply (4 + -6i) * (5 + -4i)
(4(5 + -4i) + -6i * (5 + -4i)) = 0
((5 * 4 + -4i * 4) + -6i * (5 + -4i)) = 0
((20 + -16i) + -6i * (5 + -4i)) = 0
(20 + -16i + (5 * -6i + -4i * -6i)) = 0
(20 + -16i + (-30i + 24i2)) = 0

Combine like terms: -16i + -30i = -46i
(20 + -46i + 24i2) = 0

Solving
20 + -46i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -23i + 12i2) = 0

Factor a trinomial.
2((2 + -3i)(5 + -4i)) = 0

Ignore the factor 2.

Subproblem 1
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 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 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 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Solution
i = {0.6666666667, 1.25}

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