(11-12i)(-4+6i)=0

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Solution for (11-12i)(-4+6i)=0 equation: 


Simplifying
(11 + -12i)(-4 + 6i) = 0

Multiply (11 + -12i) * (-4 + 6i)
(11(-4 + 6i) + -12i * (-4 + 6i)) = 0
((-4 * 11 + 6i * 11) + -12i * (-4 + 6i)) = 0
((-44 + 66i) + -12i * (-4 + 6i)) = 0
(-44 + 66i + (-4 * -12i + 6i * -12i)) = 0
(-44 + 66i + (48i + -72i2)) = 0

Combine like terms: 66i + 48i = 114i
(-44 + 114i + -72i2) = 0

Solving
-44 + 114i + -72i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + 57i + -36i2) = 0

Factor a trinomial.
2((-11 + 12i)(2 + -3i)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-11 + 12i)' equal to zero and attempt to solve:

Simplifying
-11 + 12i = 0

Solving
-11 + 12i = 0

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

Add '11' to each side of the equation.
-11 + 11 + 12i = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 12i = 0 + 11
12i = 0 + 11

Combine like terms: 0 + 11 = 11
12i = 11

Divide each side by '12'.
i = 0.9166666667

Simplifying
i = 0.9166666667

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 = {0.9166666667, 0.6666666667}

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