(7-6i)(2-3i)=0

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Solution for (7-6i)(2-3i)=0 equation: 


Simplifying
(7 + -6i)(2 + -3i) = 0

Multiply (7 + -6i) * (2 + -3i)
(7(2 + -3i) + -6i * (2 + -3i)) = 0
((2 * 7 + -3i * 7) + -6i * (2 + -3i)) = 0
((14 + -21i) + -6i * (2 + -3i)) = 0
(14 + -21i + (2 * -6i + -3i * -6i)) = 0
(14 + -21i + (-12i + 18i2)) = 0

Combine like terms: -21i + -12i = -33i
(14 + -33i + 18i2) = 0

Solving
14 + -33i + 18i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -3i)(7 + -6i) = 0


Subproblem 1
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

Subproblem 2
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
Solution
i = {0.6666666667, 1.166666667}

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