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

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

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

Reorder the terms:
(2 + 5i)(7i + 3) = 0

Reorder the terms:
(2 + 5i)(3 + 7i) = 0

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

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

Solving
6 + 29i + 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}