10(3-2i)(4+2i)=0

Solution for 10(3-2i)(4+2i)=0 equation:

Simplifying
10(3 + -2i)(4 + 2i) = 0

Multiply (3 + -2i) * (4 + 2i)
10(3(4 + 2i) + -2i * (4 + 2i)) = 0
10((4 * 3 + 2i * 3) + -2i * (4 + 2i)) = 0
10((12 + 6i) + -2i * (4 + 2i)) = 0
10(12 + 6i + (4 * -2i + 2i * -2i)) = 0
10(12 + 6i + (-8i + -4i2)) = 0

Combine like terms: 6i + -8i = -2i
10(12 + -2i + -4i2) = 0
(12 * 10 + -2i * 10 + -4i2 * 10) = 0
(120 + -20i + -40i2) = 0

Solving
120 + -20i + -40i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '20'.
20(6 + -1i + -2i2) = 0

Factor a trinomial.
20((3 + -2i)(2 + i)) = 0

Ignore the factor 20.
Subproblem 1
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
Subproblem 2
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
Solution
i = {1.5, -2}