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

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

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

Multiply (3 + -2i) * (-4 + 5i)
2(3(-4 + 5i) + -2i * (-4 + 5i)) = 0
2((-4 * 3 + 5i * 3) + -2i * (-4 + 5i)) = 0
2((-12 + 15i) + -2i * (-4 + 5i)) = 0
2(-12 + 15i + (-4 * -2i + 5i * -2i)) = 0
2(-12 + 15i + (8i + -10i2)) = 0

Combine like terms: 15i + 8i = 23i
2(-12 + 23i + -10i2) = 0
(-12 * 2 + 23i * 2 + -10i2 * 2) = 0
(-24 + 46i + -20i2) = 0

Solving
-24 + 46i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 23i + -10i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 2i)' equal to zero and attempt to solve:

Simplifying
-3 + 2i = 0

Solving
-3 + 2i = 0

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

Add '3' to each side of the equation.
-3 + 3 + 2i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2i = 0 + 3
2i = 0 + 3

Combine like terms: 0 + 3 = 3
2i = 3

Divide each side by '2'.
i = 1.5

Simplifying
i = 1.5
Subproblem 2
Set the factor '(4 + -5i)' equal to zero and attempt to solve:

Simplifying
4 + -5i = 0

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

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

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

Divide each side by '-5'.
i = 0.8

Simplifying
i = 0.8
Solution
i = {1.5, 0.8}