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

Solution for (3-5i)(2+7i)=0 equation:

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

Multiply (3 + -5i) * (2 + 7i)
(3(2 + 7i) + -5i * (2 + 7i)) = 0
((2 * 3 + 7i * 3) + -5i * (2 + 7i)) = 0
((6 + 21i) + -5i * (2 + 7i)) = 0
(6 + 21i + (2 * -5i + 7i * -5i)) = 0
(6 + 21i + (-10i + -35i2)) = 0

Combine like terms: 21i + -10i = 11i
(6 + 11i + -35i2) = 0

Solving
6 + 11i + -35i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + -5i)(2 + 7i) = 0

Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve:

Simplifying
3 + -5i = 0

Solving
3 + -5i = 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 + -5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5i = 0 + -3
-5i = 0 + -3

Combine like terms: 0 + -3 = -3
-5i = -3

Divide each side by '-5'.
i = 0.6

Simplifying
i = 0.6
Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve:

Simplifying
2 + 7i = 0

Solving
2 + 7i = 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 + 7i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7i = 0 + -2
7i = 0 + -2

Combine like terms: 0 + -2 = -2
7i = -2

Divide each side by '7'.
i = -0.2857142857

Simplifying
i = -0.2857142857
Solution
i = {0.6, -0.2857142857}