6(-7+6i)(-4+2i)=0

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Solution for 6(-7+6i)(-4+2i)=0 equation: 


Simplifying
6(-7 + 6i)(-4 + 2i) = 0

Multiply (-7 + 6i) * (-4 + 2i)
6(-7(-4 + 2i) + 6i * (-4 + 2i)) = 0
6((-4 * -7 + 2i * -7) + 6i * (-4 + 2i)) = 0
6((28 + -14i) + 6i * (-4 + 2i)) = 0
6(28 + -14i + (-4 * 6i + 2i * 6i)) = 0
6(28 + -14i + (-24i + 12i2)) = 0

Combine like terms: -14i + -24i = -38i
6(28 + -38i + 12i2) = 0
(28 * 6 + -38i * 6 + 12i2 * 6) = 0
(168 + -228i + 72i2) = 0

Solving
168 + -228i + 72i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '12'.
12(14 + -19i + 6i2) = 0

Factor a trinomial.
12((7 + -6i)(2 + -1i)) = 0

Ignore the factor 12.

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

Simplifying
7 + -6i = 0

Solving
7 + -6i = 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 + -6i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6i = 0 + -7
-6i = 0 + -7

Combine like terms: 0 + -7 = -7
-6i = -7

Divide each side by '-6'.
i = 1.166666667

Simplifying
i = 1.166666667

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

Simplifying
2 + -1i = 0

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

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

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

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {1.166666667, 2}

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