(3+6i)(4-7i)=0

Solution for (3+6i)(4-7i)=0 equation:

Simplifying
(3 + 6i)(4 + -7i) = 0

Multiply (3 + 6i) * (4 + -7i)
(3(4 + -7i) + 6i * (4 + -7i)) = 0
((4 * 3 + -7i * 3) + 6i * (4 + -7i)) = 0
((12 + -21i) + 6i * (4 + -7i)) = 0
(12 + -21i + (4 * 6i + -7i * 6i)) = 0
(12 + -21i + (24i + -42i2)) = 0

Combine like terms: -21i + 24i = 3i
(12 + 3i + -42i2) = 0

Solving
12 + 3i + -42i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + i + -14i2) = 0

Factor a trinomial.
3((4 + -7i)(1 + 2i)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -7i)' equal to zero and attempt to solve:

Simplifying
4 + -7i = 0

Solving
4 + -7i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -7i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7i = 0 + -4
-7i = 0 + -4

Combine like terms: 0 + -4 = -4
-7i = -4

Divide each side by '-7'.
i = 0.5714285714

Simplifying
i = 0.5714285714
Subproblem 2
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
Solution
i = {0.5714285714, -0.5}