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

Solution for (-2+i)(3-7i)=0 equation:

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

Multiply (-2 + i) * (3 + -7i)
(-2(3 + -7i) + i(3 + -7i)) = 0
((3 * -2 + -7i * -2) + i(3 + -7i)) = 0
((-6 + 14i) + i(3 + -7i)) = 0
(-6 + 14i + (3 * i + -7i * i)) = 0
(-6 + 14i + (3i + -7i2)) = 0

Combine like terms: 14i + 3i = 17i
(-6 + 17i + -7i2) = 0

Solving
-6 + 17i + -7i2 = 0

Solving for variable 'i'.

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

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

Simplifying
-2 + i = 0

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

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

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

Simplifying
i = 2
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 = {2, 0.4285714286}