(6+8i)(4-7i)=

Solution for (6+8i)(4-7i)= equation:

Simplifying
(6 + 8i)(4 + -7i) = 0

Multiply (6 + 8i) * (4 + -7i)
(6(4 + -7i) + 8i * (4 + -7i)) = 0
((4 * 6 + -7i * 6) + 8i * (4 + -7i)) = 0
((24 + -42i) + 8i * (4 + -7i)) = 0
(24 + -42i + (4 * 8i + -7i * 8i)) = 0
(24 + -42i + (32i + -56i2)) = 0

Combine like terms: -42i + 32i = -10i
(24 + -10i + -56i2) = 0

Solving
24 + -10i + -56i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -5i + -28i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -7i)' equal to zero and attempt to solve:

Simplifying
4 + -7i = 0

Solving
4 + -7i = 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 + -7i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -7i = 0 + -4
-7i = 0 + -4

Combine like terms: 0 + -4 = -4
-7i = -4

Divide each side by '-7'.
i = 0.5714285714

Simplifying
i = 0.5714285714
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 = {0.5714285714, -0.75}