0=(x^2-i^2)(x^2-25i^2)

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Solution for 0=(x^2-i^2)(x^2-25i^2) equation: 


Simplifying
0 = (x2 + -1i2)(x2 + -25i2)

Reorder the terms:
0 = (-1i2 + x2)(x2 + -25i2)

Reorder the terms:
0 = (-1i2 + x2)(-25i2 + x2)

Multiply (-1i2 + x2) * (-25i2 + x2)
0 = (-1i2 * (-25i2 + x2) + x2(-25i2 + x2))
0 = ((-25i2 * -1i2 + x2 * -1i2) + x2(-25i2 + x2))

Reorder the terms:
0 = ((-1i2x2 + 25i4) + x2(-25i2 + x2))
0 = ((-1i2x2 + 25i4) + x2(-25i2 + x2))
0 = (-1i2x2 + 25i4 + (-25i2 * x2 + x2 * x2))
0 = (-1i2x2 + 25i4 + (-25i2x2 + x4))

Reorder the terms:
0 = (-1i2x2 + -25i2x2 + 25i4 + x4)

Combine like terms: -1i2x2 + -25i2x2 = -26i2x2
0 = (-26i2x2 + 25i4 + x4)

Solving
0 = -26i2x2 + 25i4 + x4

Solving for variable 'i'.
Remove the zero:
26i2x2 + -25i4 + -1x4 = -26i2x2 + 25i4 + x4 + 26i2x2 + -25i4 + -1x4

Reorder the terms:
26i2x2 + -25i4 + -1x4 = -26i2x2 + 26i2x2 + 25i4 + -25i4 + x4 + -1x4

Combine like terms: -26i2x2 + 26i2x2 = 0
26i2x2 + -25i4 + -1x4 = 0 + 25i4 + -25i4 + x4 + -1x4
26i2x2 + -25i4 + -1x4 = 25i4 + -25i4 + x4 + -1x4

Combine like terms: 25i4 + -25i4 = 0
26i2x2 + -25i4 + -1x4 = 0 + x4 + -1x4
26i2x2 + -25i4 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
26i2x2 + -25i4 + -1x4 = 0

Factor a trinomial.
(-25i2 + x2)(i2 + -1x2) = 0

Factor a difference between two squares.
((5i + x)(-5i + x))(i2 + -1x2) = 0

Factor a difference between two squares.
((i + x)(i + -1x))(5i + x)(-5i + x) = 0


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

Simplifying
5i + x = 0

Solving
5i + x = 0

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

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

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

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

Simplifying
i = -0.2x

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

Simplifying
-5i + x = 0

Solving
-5i + x = 0

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

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

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

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

Simplifying
i = 0.2x

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

Simplifying
i + x = 0

Solving
i + x = 0

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

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

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

Simplifying
i = -1x

Subproblem 4
Set the factor '(i + -1x)' equal to zero and attempt to solve:

Simplifying
i + -1x = 0

Solving
i + -1x = 0

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

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

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

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

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