i(2-6i)-(4+3i)=

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Solution for i(2-6i)-(4+3i)= equation: 


Simplifying
i(2 + -6i) + -1(4 + 3i) = 0
(2 * i + -6i * i) + -1(4 + 3i) = 0
(2i + -6i2) + -1(4 + 3i) = 0
2i + -6i2 + (4 * -1 + 3i * -1) = 0
2i + -6i2 + (-4 + -3i) = 0

Reorder the terms:
-4 + 2i + -3i + -6i2 = 0

Combine like terms: 2i + -3i = -1i
-4 + -1i + -6i2 = 0

Solving
-4 + -1i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + i + 6i2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4 + i + 6i2)' equal to zero and attempt to solve:

Simplifying
4 + i + 6i2 = 0

Solving
4 + i + 6i2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
0.6666666667 + 0.1666666667i + i2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.1666666667i + -0.6666666667 + i2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.1666666667i + i2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.1666666667i + i2 = 0 + -0.6666666667
0.1666666667i + i2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.1666666667i + i2 = -0.6666666667

The i term is i.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1666666667i + 0.25 + i2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667i + i2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + 0.1666666667i + i2 = -0.4166666667

Factor a perfect square on the left side:
(i + 0.5)(i + 0.5) = -0.4166666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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