(6+8i)(4-6i)=

Solution for (6+8i)(4-6i)= equation:

Simplifying
(6 + 8i)(4 + -6i) = 0

Multiply (6 + 8i) * (4 + -6i)
(6(4 + -6i) + 8i * (4 + -6i)) = 0
((4 * 6 + -6i * 6) + 8i * (4 + -6i)) = 0
((24 + -36i) + 8i * (4 + -6i)) = 0
(24 + -36i + (4 * 8i + -6i * 8i)) = 0
(24 + -36i + (32i + -48i2)) = 0

Combine like terms: -36i + 32i = -4i
(24 + -4i + -48i2) = 0

Solving
24 + -4i + -48i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -1i + -12i2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve:

Simplifying
2 + -3i = 0

Solving
2 + -3i = 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 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
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 = {0.6666666667, -0.75}