(x^2+5i)(x^2+i)=0

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Solution for (x^2+5i)(x^2+i)=0 equation: 


Simplifying
(x2 + 5i)(x2 + i) = 0

Reorder the terms:
(5i + x2)(x2 + i) = 0

Reorder the terms:
(5i + x2)(i + x2) = 0

Multiply (5i + x2) * (i + x2)
(5i * (i + x2) + x2(i + x2)) = 0
((i * 5i + x2 * 5i) + x2(i + x2)) = 0

Reorder the terms:
((5ix2 + 5i2) + x2(i + x2)) = 0
((5ix2 + 5i2) + x2(i + x2)) = 0
(5ix2 + 5i2 + (i * x2 + x2 * x2)) = 0
(5ix2 + 5i2 + (ix2 + x4)) = 0

Reorder the terms:
(5ix2 + ix2 + 5i2 + x4) = 0

Combine like terms: 5ix2 + ix2 = 6ix2
(6ix2 + 5i2 + x4) = 0

Solving
6ix2 + 5i2 + x4 = 0

Solving for variable 'i'.

Factor a trinomial.
(5i + x2)(i + x2) = 0


Subproblem 1
Set the factor '(5i + x2)' equal to zero and attempt to solve:

Simplifying
5i + x2 = 0

Solving
5i + x2 = 0

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

Add '-1x2' to each side of the equation.
5i + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
5i + 0 = 0 + -1x2
5i = 0 + -1x2
Remove the zero:
5i = -1x2

Divide each side by '5'.
i = -0.2x2

Simplifying
i = -0.2x2

Subproblem 2
Set the factor '(i + x2)' equal to zero and attempt to solve:

Simplifying
i + x2 = 0

Solving
i + x2 = 0

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

Add '-1x2' to each side of the equation.
i + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
i + 0 = 0 + -1x2
i = 0 + -1x2
Remove the zero:
i = -1x2

Simplifying
i = -1x2
Solution
i = {-0.2x2, -1x2}

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