(6+7i)(4-2i)=

Solution for (6+7i)(4-2i)= equation:

Simplifying
(6 + 7i)(4 + -2i) = 0

Multiply (6 + 7i) * (4 + -2i)
(6(4 + -2i) + 7i * (4 + -2i)) = 0
((4 * 6 + -2i * 6) + 7i * (4 + -2i)) = 0
((24 + -12i) + 7i * (4 + -2i)) = 0
(24 + -12i + (4 * 7i + -2i * 7i)) = 0
(24 + -12i + (28i + -14i2)) = 0

Combine like terms: -12i + 28i = 16i
(24 + 16i + -14i2) = 0

Solving
24 + 16i + -14i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 8i + -7i2) = 0

Factor a trinomial.
2((2 + -1i)(6 + 7i)) = 0

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

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

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

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Subproblem 2
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
Solution
i = {2, -0.8571428571}