(7-8i)(4-6i)=0

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Solution for (7-8i)(4-6i)=0 equation: 


Simplifying
(7 + -8i)(4 + -6i) = 0

Multiply (7 + -8i) * (4 + -6i)
(7(4 + -6i) + -8i * (4 + -6i)) = 0
((4 * 7 + -6i * 7) + -8i * (4 + -6i)) = 0
((28 + -42i) + -8i * (4 + -6i)) = 0
(28 + -42i + (4 * -8i + -6i * -8i)) = 0
(28 + -42i + (-32i + 48i2)) = 0

Combine like terms: -42i + -32i = -74i
(28 + -74i + 48i2) = 0

Solving
28 + -74i + 48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -37i + 24i2) = 0

Factor a trinomial.
2((2 + -3i)(7 + -8i)) = 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 '(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 = {0.6666666667, 0.875}

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