(-1-4i)(-1+4i)=-16x^2+1

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Solution for (-1-4i)(-1+4i)=-16x^2+1 equation: 


Simplifying
(-1 + -4i)(-1 + 4i) = -16x2 + 1

Multiply (-1 + -4i) * (-1 + 4i)
(-1(-1 + 4i) + -4i * (-1 + 4i)) = -16x2 + 1
((-1 * -1 + 4i * -1) + -4i * (-1 + 4i)) = -16x2 + 1
((1 + -4i) + -4i * (-1 + 4i)) = -16x2 + 1
(1 + -4i + (-1 * -4i + 4i * -4i)) = -16x2 + 1
(1 + -4i + (4i + -16i2)) = -16x2 + 1

Combine like terms: -4i + 4i = 0
(1 + 0 + -16i2) = -16x2 + 1
(1 + -16i2) = -16x2 + 1

Reorder the terms:
1 + -16i2 = 1 + -16x2

Add '-1' to each side of the equation.
1 + -1 + -16i2 = 1 + -1 + -16x2

Combine like terms: 1 + -1 = 0
0 + -16i2 = 1 + -1 + -16x2
-16i2 = 1 + -1 + -16x2

Combine like terms: 1 + -1 = 0
-16i2 = 0 + -16x2
-16i2 = -16x2

Solving
-16i2 = -16x2

Solving for variable 'i'.

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

Divide each side by '-16'.
i2 = x2

Simplifying
i2 = x2

Take the square root of each side:
i = {-1x, x}

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