(-3+6i)(1+i)=

Solution for (-3+6i)(1+i)= equation:

Simplifying
(-3 + 6i)(1 + i) = 0

Multiply (-3 + 6i) * (1 + i)
(-3(1 + i) + 6i * (1 + i)) = 0
((1 * -3 + i * -3) + 6i * (1 + i)) = 0
((-3 + -3i) + 6i * (1 + i)) = 0
(-3 + -3i + (1 * 6i + i * 6i)) = 0
(-3 + -3i + (6i + 6i2)) = 0

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

Solving
-3 + 3i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + i + 2i2) = 0

Factor a trinomial.
3((-1 + -1i)(1 + -2i)) = 0

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

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Solution
i = {-1, 0.5}