(5-2i)(3+7i)=

Solution for (5-2i)(3+7i)= equation:

Simplifying
(5 + -2i)(3 + 7i) = 0

Multiply (5 + -2i) * (3 + 7i)
(5(3 + 7i) + -2i * (3 + 7i)) = 0
((3 * 5 + 7i * 5) + -2i * (3 + 7i)) = 0
((15 + 35i) + -2i * (3 + 7i)) = 0
(15 + 35i + (3 * -2i + 7i * -2i)) = 0
(15 + 35i + (-6i + -14i2)) = 0

Combine like terms: 35i + -6i = 29i
(15 + 29i + -14i2) = 0

Solving
15 + 29i + -14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -2i)(3 + 7i) = 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 + 7i)' equal to zero and attempt to solve:

Simplifying
3 + 7i = 0

Solving
3 + 7i = 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 + 7i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7i = 0 + -3
7i = 0 + -3

Combine like terms: 0 + -3 = -3
7i = -3

Divide each side by '7'.
i = -0.4285714286

Simplifying
i = -0.4285714286
Solution
i = {2.5, -0.4285714286}