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

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

Simplifying
(4 + -1i)(3 + 7i) = 0

Multiply (4 + -1i) * (3 + 7i)
(4(3 + 7i) + -1i * (3 + 7i)) = 0
((3 * 4 + 7i * 4) + -1i * (3 + 7i)) = 0
((12 + 28i) + -1i * (3 + 7i)) = 0
(12 + 28i + (3 * -1i + 7i * -1i)) = 0
(12 + 28i + (-3i + -7i2)) = 0

Combine like terms: 28i + -3i = 25i
(12 + 25i + -7i2) = 0

Solving
12 + 25i + -7i2 = 0

Solving for variable 'i'.

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

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

Simplifying
4 + -1i = 0

Solving
4 + -1i = 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 + -1i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1i = 0 + -4
-1i = 0 + -4

Combine like terms: 0 + -4 = -4
-1i = -4

Divide each side by '-1'.
i = 4

Simplifying
i = 4
Subproblem 2
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
Solution
i = {4, -0.4285714286}