(x^4+i)(x^4+25i)=0

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Solution for (x^4+i)(x^4+25i)=0 equation: 


Simplifying
(x4 + i)(x4 + 25i) = 0

Reorder the terms:
(i + x4)(x4 + 25i) = 0

Reorder the terms:
(i + x4)(25i + x4) = 0

Multiply (i + x4) * (25i + x4)
(i(25i + x4) + x4(25i + x4)) = 0
((25i * i + x4 * i) + x4(25i + x4)) = 0

Reorder the terms:
((ix4 + 25i2) + x4(25i + x4)) = 0
((ix4 + 25i2) + x4(25i + x4)) = 0
(ix4 + 25i2 + (25i * x4 + x4 * x4)) = 0
(ix4 + 25i2 + (25ix4 + x8)) = 0

Reorder the terms:
(ix4 + 25ix4 + 25i2 + x8) = 0

Combine like terms: ix4 + 25ix4 = 26ix4
(26ix4 + 25i2 + x8) = 0

Solving
26ix4 + 25i2 + x8 = 0

Solving for variable 'i'.

Factor a trinomial.
(25i + x4)(i + x4) = 0


Subproblem 1
Set the factor '(25i + x4)' equal to zero and attempt to solve:

Simplifying
25i + x4 = 0

Solving
25i + x4 = 0

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

Add '-1x4' to each side of the equation.
25i + x4 + -1x4 = 0 + -1x4

Combine like terms: x4 + -1x4 = 0
25i + 0 = 0 + -1x4
25i = 0 + -1x4
Remove the zero:
25i = -1x4

Divide each side by '25'.
i = -0.04x4

Simplifying
i = -0.04x4

Subproblem 2
Set the factor '(i + x4)' equal to zero and attempt to solve:

Simplifying
i + x4 = 0

Solving
i + x4 = 0

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

Add '-1x4' to each side of the equation.
i + x4 + -1x4 = 0 + -1x4

Combine like terms: x4 + -1x4 = 0
i + 0 = 0 + -1x4
i = 0 + -1x4
Remove the zero:
i = -1x4

Simplifying
i = -1x4
Solution
i = {-0.04x4, -1x4}

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