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

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

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

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

Combine like terms: 15i + -14i = 1i
(-6 + 1i + 35i2) = 0

Solving
-6 + 1i + 35i2 = 0

Solving for variable 'i'.

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

Subproblem 1
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
Subproblem 2
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
Solution
i = {-0.4285714286, 0.4}