(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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