(2-5i)(4+6i)=0

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Solution for (2-5i)(4+6i)=0 equation: 


Simplifying
(2 + -5i)(4 + 6i) = 0

Multiply (2 + -5i) * (4 + 6i)
(2(4 + 6i) + -5i * (4 + 6i)) = 0
((4 * 2 + 6i * 2) + -5i * (4 + 6i)) = 0
((8 + 12i) + -5i * (4 + 6i)) = 0
(8 + 12i + (4 * -5i + 6i * -5i)) = 0
(8 + 12i + (-20i + -30i2)) = 0

Combine like terms: 12i + -20i = -8i
(8 + -8i + -30i2) = 0

Solving
8 + -8i + -30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -4i + -15i2) = 0

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

Ignore the factor 2.

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

Simplifying
2 + -5i = 0

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

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

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

Divide each side by '-5'.
i = 0.4

Simplifying
i = 0.4

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 = {0.4, -0.6666666667}

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