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Simplifying (x + 0)(x + 7)(x + -2i)(x + 2i) = 0 Reorder the terms: (0 + x)(x + 7)(x + -2i)(x + 2i) = 0 Remove the zero: (x)(x + 7)(x + -2i)(x + 2i) = 0 Reorder the terms: x(7 + x)(x + -2i)(x + 2i) = 0 Reorder the terms: x(7 + x)(-2i + x)(x + 2i) = 0 Reorder the terms: x(7 + x)(-2i + x)(2i + x) = 0 Multiply (7 + x) * (-2i + x) x(7(-2i + x) + x(-2i + x))(2i + x) = 0 x((-2i * 7 + x * 7) + x(-2i + x))(2i + x) = 0 x((-14i + 7x) + x(-2i + x))(2i + x) = 0 x(-14i + 7x + (-2i * x + x * x))(2i + x) = 0 x(-14i + 7x + (-2ix + x2))(2i + x) = 0 Reorder the terms: x(-14i + -2ix + 7x + x2)(2i + x) = 0 x(-14i + -2ix + 7x + x2)(2i + x) = 0 Multiply (-14i + -2ix + 7x + x2) * (2i + x) x(-14i * (2i + x) + -2ix * (2i + x) + 7x * (2i + x) + x2(2i + x)) = 0 x((2i * -14i + x * -14i) + -2ix * (2i + x) + 7x * (2i + x) + x2(2i + x)) = 0 Reorder the terms: x((-14ix + -28i2) + -2ix * (2i + x) + 7x * (2i + x) + x2(2i + x)) = 0 x((-14ix + -28i2) + -2ix * (2i + x) + 7x * (2i + x) + x2(2i + x)) = 0 x(-14ix + -28i2 + (2i * -2ix + x * -2ix) + 7x * (2i + x) + x2(2i + x)) = 0 Reorder the terms: x(-14ix + -28i2 + (-2ix2 + -4i2x) + 7x * (2i + x) + x2(2i + x)) = 0 x(-14ix + -28i2 + (-2ix2 + -4i2x) + 7x * (2i + x) + x2(2i + x)) = 0 x(-14ix + -28i2 + -2ix2 + -4i2x + (2i * 7x + x * 7x) + x2(2i + x)) = 0 x(-14ix + -28i2 + -2ix2 + -4i2x + (14ix + 7x2) + x2(2i + x)) = 0 x(-14ix + -28i2 + -2ix2 + -4i2x + 14ix + 7x2 + (2i * x2 + x * x2)) = 0 x(-14ix + -28i2 + -2ix2 + -4i2x + 14ix + 7x2 + (2ix2 + x3)) = 0 Reorder the terms: x(-14ix + 14ix + -2ix2 + 2ix2 + -28i2 + -4i2x + 7x2 + x3) = 0 Combine like terms: -14ix + 14ix = 0 x(0 + -2ix2 + 2ix2 + -28i2 + -4i2x + 7x2 + x3) = 0 x(-2ix2 + 2ix2 + -28i2 + -4i2x + 7x2 + x3) = 0 Combine like terms: -2ix2 + 2ix2 = 0 x(0 + -28i2 + -4i2x + 7x2 + x3) = 0 x(-28i2 + -4i2x + 7x2 + x3) = 0 (-28i2 * x + -4i2x * x + 7x2 * x + x3 * x) = 0 (-28i2x + -4i2x2 + 7x3 + x4) = 0 Solving -28i2x + -4i2x2 + 7x3 + x4 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-7x3' to each side of the equation. -28i2x + -4i2x2 + 7x3 + -7x3 + x4 = 0 + -7x3 Combine like terms: 7x3 + -7x3 = 0 -28i2x + -4i2x2 + 0 + x4 = 0 + -7x3 -28i2x + -4i2x2 + x4 = 0 + -7x3 Remove the zero: -28i2x + -4i2x2 + x4 = -7x3 Add '-1x4' to each side of the equation. -28i2x + -4i2x2 + x4 + -1x4 = -7x3 + -1x4 Combine like terms: x4 + -1x4 = 0 -28i2x + -4i2x2 + 0 = -7x3 + -1x4 -28i2x + -4i2x2 = -7x3 + -1x4 Reorder the terms: -28i2x + -4i2x2 + 7x3 + x4 = -7x3 + 7x3 + -1x4 + x4 Combine like terms: -7x3 + 7x3 = 0 -28i2x + -4i2x2 + 7x3 + x4 = 0 + -1x4 + x4 -28i2x + -4i2x2 + 7x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -28i2x + -4i2x2 + 7x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-28i2 + -4i2x + 7x2 + x3) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-28i2 + -4i2x + 7x2 + x3)' equal to zero and attempt to solve: Simplifying -28i2 + -4i2x + 7x2 + x3 = 0 Solving -28i2 + -4i2x + 7x2 + x3 = 0 Move all terms containing i to the left, all other terms to the right. Add '-7x2' to each side of the equation. -28i2 + -4i2x + 7x2 + -7x2 + x3 = 0 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -28i2 + -4i2x + 0 + x3 = 0 + -7x2 -28i2 + -4i2x + x3 = 0 + -7x2 Remove the zero: -28i2 + -4i2x + x3 = -7x2 Add '-1x3' to each side of the equation. -28i2 + -4i2x + x3 + -1x3 = -7x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -28i2 + -4i2x + 0 = -7x2 + -1x3 -28i2 + -4i2x = -7x2 + -1x3 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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