(6+4i)(1-7i)=

Solution for (6+4i)(1-7i)= equation:

Simplifying
(6 + 4i)(1 + -7i) = 0

Multiply (6 + 4i) * (1 + -7i)
(6(1 + -7i) + 4i * (1 + -7i)) = 0
((1 * 6 + -7i * 6) + 4i * (1 + -7i)) = 0
((6 + -42i) + 4i * (1 + -7i)) = 0
(6 + -42i + (1 * 4i + -7i * 4i)) = 0
(6 + -42i + (4i + -28i2)) = 0

Combine like terms: -42i + 4i = -38i
(6 + -38i + -28i2) = 0

Solving
6 + -38i + -28i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -19i + -14i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -7i)' equal to zero and attempt to solve:

Simplifying
1 + -7i = 0

Solving
1 + -7i = 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 + -7i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7i = 0 + -1
-7i = 0 + -1

Combine like terms: 0 + -1 = -1
-7i = -1

Divide each side by '-7'.
i = 0.1428571429

Simplifying
i = 0.1428571429
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 = {0.1428571429, -1.5}