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

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


Simplifying
(4 + -2i) * x(2 + 7i) = 0

Reorder the terms for easier multiplication:
x(4 + -2i)(2 + 7i) = 0

Multiply (4 + -2i) * (2 + 7i)
x(4(2 + 7i) + -2i * (2 + 7i)) = 0
x((2 * 4 + 7i * 4) + -2i * (2 + 7i)) = 0
x((8 + 28i) + -2i * (2 + 7i)) = 0
x(8 + 28i + (2 * -2i + 7i * -2i)) = 0
x(8 + 28i + (-4i + -14i2)) = 0

Combine like terms: 28i + -4i = 24i
x(8 + 24i + -14i2) = 0
(8 * x + 24i * x + -14i2 * x) = 0

Reorder the terms:
(24ix + -14i2x + 8x) = 0
(24ix + -14i2x + 8x) = 0

Solving
24ix + -14i2x + 8x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(12i + -7i2 + 4) = 0

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

Ignore the factor 2.

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 '(-7i + -2)' equal to zero and attempt to solve:

Simplifying
-7i + -2 = 0

Reorder the terms:
-2 + -7i = 0

Solving
-2 + -7i = 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 + -7i = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7i = 0 + 2
-7i = 0 + 2

Combine like terms: 0 + 2 = 2
-7i = 2

Divide each side by '-7'.
i = -0.2857142857

Simplifying
i = -0.2857142857

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

Simplifying
i + -2 = 0

Reorder the terms:
-2 + i = 0

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

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

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

Simplifying
i = 2
Solution
i = {-0.2857142857, 2}

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