(x-2)(x+10)(4+4i)(4-4i)=

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Solution for (x-2)(x+10)(4+4i)(4-4i)= equation:


Simplifying
(x + -2)(x + 10)(4 + 4i)(4 + -4i) = 0

Reorder the terms:
(-2 + x)(x + 10)(4 + 4i)(4 + -4i) = 0

Reorder the terms:
(-2 + x)(10 + x)(4 + 4i)(4 + -4i) = 0

Multiply (-2 + x) * (10 + x)
(-2(10 + x) + x(10 + x))(4 + 4i)(4 + -4i) = 0
((10 * -2 + x * -2) + x(10 + x))(4 + 4i)(4 + -4i) = 0
((-20 + -2x) + x(10 + x))(4 + 4i)(4 + -4i) = 0
(-20 + -2x + (10 * x + x * x))(4 + 4i)(4 + -4i) = 0
(-20 + -2x + (10x + x2))(4 + 4i)(4 + -4i) = 0

Combine like terms: -2x + 10x = 8x
(-20 + 8x + x2)(4 + 4i)(4 + -4i) = 0

Multiply (-20 + 8x + x2) * (4 + 4i)
(-20(4 + 4i) + 8x * (4 + 4i) + x2(4 + 4i))(4 + -4i) = 0
((4 * -20 + 4i * -20) + 8x * (4 + 4i) + x2(4 + 4i))(4 + -4i) = 0
((-80 + -80i) + 8x * (4 + 4i) + x2(4 + 4i))(4 + -4i) = 0
(-80 + -80i + (4 * 8x + 4i * 8x) + x2(4 + 4i))(4 + -4i) = 0

Reorder the terms:
(-80 + -80i + (32ix + 32x) + x2(4 + 4i))(4 + -4i) = 0
(-80 + -80i + (32ix + 32x) + x2(4 + 4i))(4 + -4i) = 0
(-80 + -80i + 32ix + 32x + (4 * x2 + 4i * x2))(4 + -4i) = 0

Reorder the terms:
(-80 + -80i + 32ix + 32x + (4ix2 + 4x2))(4 + -4i) = 0
(-80 + -80i + 32ix + 32x + (4ix2 + 4x2))(4 + -4i) = 0

Reorder the terms:
(-80 + -80i + 32ix + 4ix2 + 32x + 4x2)(4 + -4i) = 0
(-80 + -80i + 32ix + 4ix2 + 32x + 4x2)(4 + -4i) = 0

Multiply (-80 + -80i + 32ix + 4ix2 + 32x + 4x2) * (4 + -4i)
(-80(4 + -4i) + -80i * (4 + -4i) + 32ix * (4 + -4i) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
((4 * -80 + -4i * -80) + -80i * (4 + -4i) + 32ix * (4 + -4i) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
((-320 + 320i) + -80i * (4 + -4i) + 32ix * (4 + -4i) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + (4 * -80i + -4i * -80i) + 32ix * (4 + -4i) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + (-320i + 320i2) + 32ix * (4 + -4i) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + (4 * 32ix + -4i * 32ix) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + (128ix + -128i2x) + 4ix2 * (4 + -4i) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + (4 * 4ix2 + -4i * 4ix2) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + (16ix2 + -16i2x2) + 32x * (4 + -4i) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + (4 * 32x + -4i * 32x) + 4x2 * (4 + -4i)) = 0

Reorder the terms:
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + (-128ix + 128x) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + (-128ix + 128x) + 4x2 * (4 + -4i)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + -128ix + 128x + (4 * 4x2 + -4i * 4x2)) = 0

Reorder the terms:
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + -128ix + 128x + (-16ix2 + 16x2)) = 0
(-320 + 320i + -320i + 320i2 + 128ix + -128i2x + 16ix2 + -16i2x2 + -128ix + 128x + (-16ix2 + 16x2)) = 0

Reorder the terms:
(-320 + 320i + -320i + 128ix + -128ix + 16ix2 + -16ix2 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0

Combine like terms: 320i + -320i = 0
(-320 + 0 + 128ix + -128ix + 16ix2 + -16ix2 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0
(-320 + 128ix + -128ix + 16ix2 + -16ix2 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0

Combine like terms: 128ix + -128ix = 0
(-320 + 0 + 16ix2 + -16ix2 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0
(-320 + 16ix2 + -16ix2 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0

Combine like terms: 16ix2 + -16ix2 = 0
(-320 + 0 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0
(-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2) = 0

Solving
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0

Solving for variable 'i'.

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

Add '320' to each side of the equation.
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 320 + 16x2 = 0 + 320

Reorder the terms:
-320 + 320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0 + 320

Combine like terms: -320 + 320 = 0
0 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0 + 320
320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0 + 320

Combine like terms: 0 + 320 = 320
320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 320

Add '-128x' to each side of the equation.
320i2 + -128i2x + -16i2x2 + 128x + -128x + 16x2 = 320 + -128x

Combine like terms: 128x + -128x = 0
320i2 + -128i2x + -16i2x2 + 0 + 16x2 = 320 + -128x
320i2 + -128i2x + -16i2x2 + 16x2 = 320 + -128x

Add '-16x2' to each side of the equation.
320i2 + -128i2x + -16i2x2 + 16x2 + -16x2 = 320 + -128x + -16x2

Combine like terms: 16x2 + -16x2 = 0
320i2 + -128i2x + -16i2x2 + 0 = 320 + -128x + -16x2
320i2 + -128i2x + -16i2x2 = 320 + -128x + -16x2

Reorder the terms:
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 320 + -128x + -16x2 + -320 + 128x + 16x2

Reorder the terms:
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 320 + -320 + -128x + 128x + -16x2 + 16x2

Combine like terms: 320 + -320 = 0
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0 + -128x + 128x + -16x2 + 16x2
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = -128x + 128x + -16x2 + 16x2

Combine like terms: -128x + 128x = 0
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0 + -16x2 + 16x2
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-320 + 320i2 + -128i2x + -16i2x2 + 128x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-20 + 20i2 + -8i2x + -1i2x2 + 8x + x2) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-20 + 20i2 + -8i2x + -1i2x2 + 8x + x2)' equal to zero and attempt to solve: Simplifying -20 + 20i2 + -8i2x + -1i2x2 + 8x + x2 = 0 Solving -20 + 20i2 + -8i2x + -1i2x2 + 8x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20i2 + -8i2x + -1i2x2 + 8x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 20i2 + -8i2x + -1i2x2 + 8x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 20i2 + -8i2x + -1i2x2 + 8x + x2 = 0 + 20 20i2 + -8i2x + -1i2x2 + 8x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 20i2 + -8i2x + -1i2x2 + 8x + x2 = 20 Add '-8x' to each side of the equation. 20i2 + -8i2x + -1i2x2 + 8x + -8x + x2 = 20 + -8x Combine like terms: 8x + -8x = 0 20i2 + -8i2x + -1i2x2 + 0 + x2 = 20 + -8x 20i2 + -8i2x + -1i2x2 + x2 = 20 + -8x Add '-1x2' to each side of the equation. 20i2 + -8i2x + -1i2x2 + x2 + -1x2 = 20 + -8x + -1x2 Combine like terms: x2 + -1x2 = 0 20i2 + -8i2x + -1i2x2 + 0 = 20 + -8x + -1x2 20i2 + -8i2x + -1i2x2 = 20 + -8x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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