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

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


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

Reorder the terms:
(2 + 2i)(4i + -5) = 0

Reorder the terms:
(2 + 2i)(-5 + 4i) = 0

Multiply (2 + 2i) * (-5 + 4i)
(2(-5 + 4i) + 2i * (-5 + 4i)) = 0
((-5 * 2 + 4i * 2) + 2i * (-5 + 4i)) = 0
((-10 + 8i) + 2i * (-5 + 4i)) = 0
(-10 + 8i + (-5 * 2i + 4i * 2i)) = 0
(-10 + 8i + (-10i + 8i2)) = 0

Combine like terms: 8i + -10i = -2i
(-10 + -2i + 8i2) = 0

Solving
-10 + -2i + 8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1i + 4i2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -1i = 0

Solving
-1 + -1i = 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 + -1i = 0 + 1

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

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

Divide each side by '-1'.
i = -1

Simplifying
i = -1

Subproblem 2
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 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 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Solution
i = {-1, 1.25}

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