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

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


Simplifying
(x + -2i)(x + i) = 0

Reorder the terms:
(-2i + x)(x + i) = 0

Reorder the terms:
(-2i + x)(i + x) = 0

Multiply (-2i + x) * (i + x)
(-2i * (i + x) + x(i + x)) = 0
((i * -2i + x * -2i) + x(i + x)) = 0

Reorder the terms:
((-2ix + -2i2) + x(i + x)) = 0
((-2ix + -2i2) + x(i + x)) = 0
(-2ix + -2i2 + (i * x + x * x)) = 0
(-2ix + -2i2 + (ix + x2)) = 0

Reorder the terms:
(-2ix + ix + -2i2 + x2) = 0

Combine like terms: -2ix + ix = -1ix
(-1ix + -2i2 + x2) = 0

Solving
-1ix + -2i2 + x2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-1i + -1x)(2i + -1x) = 0

Subproblem 1

Set the factor '(-1i + -1x)' equal to zero and attempt to solve: Simplifying -1i + -1x = 0 Solving -1i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. -1i + -1x + x = 0 + x Combine like terms: -1x + x = 0 -1i + 0 = 0 + x -1i = 0 + x Remove the zero: -1i = x Divide each side by '-1'. i = -1x Simplifying i = -1x

Subproblem 2

Set the factor '(2i + -1x)' equal to zero and attempt to solve: Simplifying 2i + -1x = 0 Solving 2i + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add 'x' to each side of the equation. 2i + -1x + x = 0 + x Combine like terms: -1x + x = 0 2i + 0 = 0 + x 2i = 0 + x Remove the zero: 2i = x Divide each side by '2'. i = 0.5x Simplifying i = 0.5x

Solution

i = {-1x, 0.5x}

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