(7+5i)(8-6i)=0

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Solution for (7+5i)(8-6i)=0 equation: 


Simplifying
(7 + 5i)(8 + -6i) = 0

Multiply (7 + 5i) * (8 + -6i)
(7(8 + -6i) + 5i * (8 + -6i)) = 0
((8 * 7 + -6i * 7) + 5i * (8 + -6i)) = 0
((56 + -42i) + 5i * (8 + -6i)) = 0
(56 + -42i + (8 * 5i + -6i * 5i)) = 0
(56 + -42i + (40i + -30i2)) = 0

Combine like terms: -42i + 40i = -2i
(56 + -2i + -30i2) = 0

Solving
56 + -2i + -30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -1i + -15i2) = 0

Factor a trinomial.
2((4 + -3i)(7 + 5i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3i)' equal to zero and attempt to solve:

Simplifying
4 + -3i = 0

Solving
4 + -3i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -3i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3i = 0 + -4
-3i = 0 + -4

Combine like terms: 0 + -4 = -4
-3i = -4

Divide each side by '-3'.
i = 1.333333333

Simplifying
i = 1.333333333

Subproblem 2
Set the factor '(7 + 5i)' equal to zero and attempt to solve:

Simplifying
7 + 5i = 0

Solving
7 + 5i = 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 + 5i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 5i = 0 + -7
5i = 0 + -7

Combine like terms: 0 + -7 = -7
5i = -7

Divide each side by '5'.
i = -1.4

Simplifying
i = -1.4
Solution
i = {1.333333333, -1.4}

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