(-5+i)x(2+3i)=

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


Simplifying
(-5 + i) * x(2 + 3i) = 0

Reorder the terms for easier multiplication:
x(-5 + i)(2 + 3i) = 0

Multiply (-5 + i) * (2 + 3i)
x(-5(2 + 3i) + i(2 + 3i)) = 0
x((2 * -5 + 3i * -5) + i(2 + 3i)) = 0
x((-10 + -15i) + i(2 + 3i)) = 0
x(-10 + -15i + (2 * i + 3i * i)) = 0
x(-10 + -15i + (2i + 3i2)) = 0

Combine like terms: -15i + 2i = -13i
x(-10 + -13i + 3i2) = 0
(-10 * x + -13i * x + 3i2 * x) = 0

Reorder the terms:
(-13ix + 3i2x + -10x) = 0
(-13ix + 3i2x + -10x) = 0

Solving
-13ix + 3i2x + -10x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-13i + 3i2 + -10) = 0

Factor a trinomial.
x((i + -5)(3i + 2)) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(i + -5)' equal to zero and attempt to solve:

Simplifying
i + -5 = 0

Reorder the terms:
-5 + i = 0

Solving
-5 + i = 0

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

Add '5' to each side of the equation.
-5 + 5 + i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + i = 0 + 5
i = 0 + 5

Combine like terms: 0 + 5 = 5
i = 5

Simplifying
i = 5

Subproblem 3
Set the factor '(3i + 2)' equal to zero and attempt to solve:

Simplifying
3i + 2 = 0

Reorder the terms:
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 = {5, -0.6666666667}

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