(2-5i)((6-3i)-(-5+9i))=

Solution for (2-5i)((6-3i)-(-5+9i))= equation:

Simplifying
(2 + -5i)((6 + -3i) + -1(-5 + 9i)) = 0

Remove parenthesis around (6 + -3i)
(2 + -5i)(6 + -3i + -1(-5 + 9i)) = 0
(2 + -5i)(6 + -3i + (-5 * -1 + 9i * -1)) = 0
(2 + -5i)(6 + -3i + (5 + -9i)) = 0

Reorder the terms:
(2 + -5i)(6 + 5 + -3i + -9i) = 0

Combine like terms: 6 + 5 = 11
(2 + -5i)(11 + -3i + -9i) = 0

Combine like terms: -3i + -9i = -12i
(2 + -5i)(11 + -12i) = 0

Multiply (2 + -5i) * (11 + -12i)
(2(11 + -12i) + -5i * (11 + -12i)) = 0
((11 * 2 + -12i * 2) + -5i * (11 + -12i)) = 0
((22 + -24i) + -5i * (11 + -12i)) = 0
(22 + -24i + (11 * -5i + -12i * -5i)) = 0
(22 + -24i + (-55i + 60i2)) = 0

Combine like terms: -24i + -55i = -79i
(22 + -79i + 60i2) = 0

Solving
22 + -79i + 60i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -5i)(11 + -12i) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(11 + -12i)' equal to zero and attempt to solve:

Simplifying
11 + -12i = 0

Solving
11 + -12i = 0

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

Add '-11' to each side of the equation.
11 + -11 + -12i = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -12i = 0 + -11
-12i = 0 + -11

Combine like terms: 0 + -11 = -11
-12i = -11

Divide each side by '-12'.
i = 0.9166666667

Simplifying
i = 0.9166666667
Solution
i = {0.4, 0.9166666667}