(4+6i)(1-i)=

Solution for (4+6i)(1-i)= equation:

Simplifying
(4 + 6i)(1 + -1i) = 0

Multiply (4 + 6i) * (1 + -1i)
(4(1 + -1i) + 6i * (1 + -1i)) = 0
((1 * 4 + -1i * 4) + 6i * (1 + -1i)) = 0
((4 + -4i) + 6i * (1 + -1i)) = 0
(4 + -4i + (1 * 6i + -1i * 6i)) = 0
(4 + -4i + (6i + -6i2)) = 0

Combine like terms: -4i + 6i = 2i
(4 + 2i + -6i2) = 0

Solving
4 + 2i + -6i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.
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 '(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
Solution
i = {1, -0.6666666667}