(3+4i)(2-7i)=

Solution for (3+4i)(2-7i)= equation:

Simplifying
(3 + 4i)(2 + -7i) = 0

Multiply (3 + 4i) * (2 + -7i)
(3(2 + -7i) + 4i * (2 + -7i)) = 0
((2 * 3 + -7i * 3) + 4i * (2 + -7i)) = 0
((6 + -21i) + 4i * (2 + -7i)) = 0
(6 + -21i + (2 * 4i + -7i * 4i)) = 0
(6 + -21i + (8i + -28i2)) = 0

Combine like terms: -21i + 8i = -13i
(6 + -13i + -28i2) = 0

Solving
6 + -13i + -28i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + -7i = 0

Solving
2 + -7i = 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 + -7i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7i = 0 + -2
-7i = 0 + -2

Combine like terms: 0 + -2 = -2
-7i = -2

Divide each side by '-7'.
i = 0.2857142857

Simplifying
i = 0.2857142857
Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {0.2857142857, -0.75}