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

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

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

Multiply (3 + 6i) * (-2 + 7i)
(3(-2 + 7i) + 6i * (-2 + 7i)) = 0
((-2 * 3 + 7i * 3) + 6i * (-2 + 7i)) = 0
((-6 + 21i) + 6i * (-2 + 7i)) = 0
(-6 + 21i + (-2 * 6i + 7i * 6i)) = 0
(-6 + 21i + (-12i + 42i2)) = 0

Combine like terms: 21i + -12i = 9i
(-6 + 9i + 42i2) = 0

Solving
-6 + 9i + 42i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + 3i + 14i2) = 0

Factor a trinomial.
3((-1 + -2i)(2 + -7i)) = 0

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

Simplifying
-1 + -2i = 0

Solving
-1 + -2i = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2i = 0 + 1
-2i = 0 + 1

Combine like terms: 0 + 1 = 1
-2i = 1

Divide each side by '-2'.
i = -0.5

Simplifying
i = -0.5
Subproblem 2
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
Solution
i = {-0.5, 0.2857142857}