-5(1+2i)+3i(3-4i)=

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Solution for -5(1+2i)+3i(3-4i)= equation: 


Simplifying
-5(1 + 2i) + 3i(3 + -4i) = 0
(1 * -5 + 2i * -5) + 3i(3 + -4i) = 0
(-5 + -10i) + 3i(3 + -4i) = 0
-5 + -10i + (3 * 3i + -4i * 3i) = 0
-5 + -10i + (9i + -12i2) = 0

Combine like terms: -10i + 9i = -1i
-5 + -1i + -12i2 = 0

Solving
-5 + -1i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + i + 12i2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(5 + i + 12i2)' equal to zero and attempt to solve:

Simplifying
5 + i + 12i2 = 0

Solving
5 + i + 12i2 = 0

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

Divide each side by '12'.
0.4166666667 + 0.08333333333i + i2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + 0.08333333333i + -0.4166666667 + i2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + 0.08333333333i + i2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + 0.08333333333i + i2 = 0 + -0.4166666667
0.08333333333i + i2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
0.08333333333i + i2 = -0.4166666667

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.
0.08333333333i + 0.25 + i2 = -0.4166666667 + 0.25

Reorder the terms:
0.25 + 0.08333333333i + i2 = -0.4166666667 + 0.25

Combine like terms: -0.4166666667 + 0.25 = -0.1666666667
0.25 + 0.08333333333i + i2 = -0.1666666667

Factor a perfect square on the left side:
(i + 0.5)(i + 0.5) = -0.1666666667

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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