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

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

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

Multiply (5 + 2i) * (-3 + 4i)
(5(-3 + 4i) + 2i * (-3 + 4i)) = 0
((-3 * 5 + 4i * 5) + 2i * (-3 + 4i)) = 0
((-15 + 20i) + 2i * (-3 + 4i)) = 0
(-15 + 20i + (-3 * 2i + 4i * 2i)) = 0
(-15 + 20i + (-6i + 8i2)) = 0

Combine like terms: 20i + -6i = 14i
(-15 + 14i + 8i2) = 0

Solving
-15 + 14i + 8i2 = 0

Solving for variable 'i'.

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

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 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 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 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75
Solution
i = {-2.5, 0.75}