(4-3i)(5+2i)=0

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Solution for (4-3i)(5+2i)=0 equation: 


Simplifying
(4 + -3i)(5 + 2i) = 0

Multiply (4 + -3i) * (5 + 2i)
(4(5 + 2i) + -3i * (5 + 2i)) = 0
((5 * 4 + 2i * 4) + -3i * (5 + 2i)) = 0
((20 + 8i) + -3i * (5 + 2i)) = 0
(20 + 8i + (5 * -3i + 2i * -3i)) = 0
(20 + 8i + (-15i + -6i2)) = 0

Combine like terms: 8i + -15i = -7i
(20 + -7i + -6i2) = 0

Solving
20 + -7i + -6i2 = 0

Solving for variable 'i'.

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


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 '(5 + 2i)' equal to zero and attempt to solve:

Simplifying
5 + 2i = 0

Solving
5 + 2i = 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 + 2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2i = 0 + -5
2i = 0 + -5

Combine like terms: 0 + -5 = -5
2i = -5

Divide each side by '2'.
i = -2.5

Simplifying
i = -2.5
Solution
i = {1.333333333, -2.5}

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