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

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

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

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

Combine like terms: -24i + 42i = 18i
(-42 + 18i + 24i2) = 0

Solving
-42 + 18i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + 3i + 4i2) = 0

Factor a trinomial.
6((-7 + -4i)(1 + -1i)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-7 + -4i)' equal to zero and attempt to solve:

Simplifying
-7 + -4i = 0

Solving
-7 + -4i = 0

Move all terms containing i to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -4i = 0 + 7

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

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

Divide each side by '-4'.
i = -1.75

Simplifying
i = -1.75
Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve:

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1i = 0 + -1
-1i = 0 + -1

Combine like terms: 0 + -1 = -1
-1i = -1

Divide each side by '-1'.
i = 1

Simplifying
i = 1
Solution
i = {-1.75, 1}