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

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

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

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

Combine like terms: -14i + 18i = 4i
(12 + 4i + -21i2) = 0

Solving
12 + 4i + -21i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + 3i = 0

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

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

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

Divide each side by '3'.
i = -0.6666666667

Simplifying
i = -0.6666666667
Solution
i = {0.8571428571, -0.6666666667}