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

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

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

Multiply (6 + 2i) * (4 + -5i)
(6(4 + -5i) + 2i * (4 + -5i)) = 0
((4 * 6 + -5i * 6) + 2i * (4 + -5i)) = 0
((24 + -30i) + 2i * (4 + -5i)) = 0
(24 + -30i + (4 * 2i + -5i * 2i)) = 0
(24 + -30i + (8i + -10i2)) = 0

Combine like terms: -30i + 8i = -22i
(24 + -22i + -10i2) = 0

Solving
24 + -22i + -10i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -11i + -5i2) = 0

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

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

Simplifying
3 + i = 0

Solving
3 + i = 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 + i = 0 + -3

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

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

Simplifying
i = -3
Solution
i = {0.8, -3}