(2i+3)(7i+6)=

Solution for (2i+3)(7i+6)= equation:

Simplifying
(2i + 3)(7i + 6) = 0

Reorder the terms:
(3 + 2i)(7i + 6) = 0

Reorder the terms:
(3 + 2i)(6 + 7i) = 0

Multiply (3 + 2i) * (6 + 7i)
(3(6 + 7i) + 2i * (6 + 7i)) = 0
((6 * 3 + 7i * 3) + 2i * (6 + 7i)) = 0
((18 + 21i) + 2i * (6 + 7i)) = 0
(18 + 21i + (6 * 2i + 7i * 2i)) = 0
(18 + 21i + (12i + 14i2)) = 0

Combine like terms: 21i + 12i = 33i
(18 + 33i + 14i2) = 0

Solving
18 + 33i + 14i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + 2i)(6 + 7i) = 0

Subproblem 1
Set the factor '(3 + 2i)' equal to zero and attempt to solve:

Simplifying
3 + 2i = 0

Solving
3 + 2i = 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 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Subproblem 2
Set the factor '(6 + 7i)' equal to zero and attempt to solve:

Simplifying
6 + 7i = 0

Solving
6 + 7i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + 7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7i = 0 + -6
7i = 0 + -6

Combine like terms: 0 + -6 = -6
7i = -6

Divide each side by '7'.
i = -0.8571428571

Simplifying
i = -0.8571428571
Solution
i = {-1.5, -0.8571428571}