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

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

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

Multiply (5 + -2i) * (6 + 2i)
(5(6 + 2i) + -2i * (6 + 2i)) = 0
((6 * 5 + 2i * 5) + -2i * (6 + 2i)) = 0
((30 + 10i) + -2i * (6 + 2i)) = 0
(30 + 10i + (6 * -2i + 2i * -2i)) = 0
(30 + 10i + (-12i + -4i2)) = 0

Combine like terms: 10i + -12i = -2i
(30 + -2i + -4i2) = 0

Solving
30 + -2i + -4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -1i + -2i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve:

Simplifying
5 + -2i = 0

Solving
5 + -2i = 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 + -2i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2i = 0 + -5
-2i = 0 + -5

Combine like terms: 0 + -5 = -5
-2i = -5

Divide each side by '-2'.
i = 2.5

Simplifying
i = 2.5
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 = {2.5, -3}