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

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

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

Multiply (6 + 4i) * (3 + -7i)
(6(3 + -7i) + 4i * (3 + -7i)) = 0
((3 * 6 + -7i * 6) + 4i * (3 + -7i)) = 0
((18 + -42i) + 4i * (3 + -7i)) = 0
(18 + -42i + (3 * 4i + -7i * 4i)) = 0
(18 + -42i + (12i + -28i2)) = 0

Combine like terms: -42i + 12i = -30i
(18 + -30i + -28i2) = 0

Solving
18 + -30i + -28i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -15i + -14i2) = 0

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

Ignore the factor 2.
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 '(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
Solution
i = {0.4285714286, -1.5}