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

Subproblem 1
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
Subproblem 2
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
Solution
i = {0.2857142857, -0.6}