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

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


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

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

Combine like terms: -20i + -8i = -28i
(-8 + -28i + -20i2) = 0

Solving
-8 + -28i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-4'.
-4(2 + 7i + 5i2) = 0

Factor a trinomial.
-4((1 + i)(2 + 5i)) = 0

Ignore the factor -4.

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

Simplifying
1 + i = 0

Solving
1 + i = 0

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

Add '-1' to each side of the equation.
1 + -1 + i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + i = 0 + -1
i = 0 + -1

Combine like terms: 0 + -1 = -1
i = -1

Simplifying
i = -1

Subproblem 2
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
Solution
i = {-1, -0.4}

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