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Simplifying 0 = (-3i + 0j + 3k) * x(-20i + 8j + -4k) Anything times zero is zero. 0 = (-3i + 0j + 3k) * x(-20i + 8j + -4k) Reorder the terms: 0 = (0 + -3i + 3k) * x(-20i + 8j + -4k) Remove the zero: 0 = (-3i + 3k) * x(-20i + 8j + -4k) Reorder the terms for easier multiplication: 0 = x(-3i + 3k)(-20i + 8j + -4k) Multiply (-3i + 3k) * (-20i + 8j + -4k) 0 = x(-3i * (-20i + 8j + -4k) + 3k * (-20i + 8j + -4k)) 0 = x((-20i * -3i + 8j * -3i + -4k * -3i) + 3k * (-20i + 8j + -4k)) Reorder the terms: 0 = x((-24ij + 12ik + 60i2) + 3k * (-20i + 8j + -4k)) 0 = x((-24ij + 12ik + 60i2) + 3k * (-20i + 8j + -4k)) 0 = x(-24ij + 12ik + 60i2 + (-20i * 3k + 8j * 3k + -4k * 3k)) 0 = x(-24ij + 12ik + 60i2 + (-60ik + 24jk + -12k2)) Reorder the terms: 0 = x(-24ij + 12ik + -60ik + 60i2 + 24jk + -12k2) Combine like terms: 12ik + -60ik = -48ik 0 = x(-24ij + -48ik + 60i2 + 24jk + -12k2) 0 = (-24ij * x + -48ik * x + 60i2 * x + 24jk * x + -12k2 * x) 0 = (-24ijx + -48ikx + 60i2x + 24jkx + -12k2x) Solving 0 = -24ijx + -48ikx + 60i2x + 24jkx + -12k2x Solving for variable 'i'. Remove the zero: 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = -24ijx + -48ikx + 60i2x + 24jkx + -12k2x + 24ijx + 48ikx + -60i2x + -24jkx + 12k2x Reorder the terms: 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = -24ijx + 24ijx + -48ikx + 48ikx + 60i2x + -60i2x + 24jkx + -24jkx + -12k2x + 12k2x Combine like terms: -24ijx + 24ijx = 0 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 0 + -48ikx + 48ikx + 60i2x + -60i2x + 24jkx + -24jkx + -12k2x + 12k2x 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = -48ikx + 48ikx + 60i2x + -60i2x + 24jkx + -24jkx + -12k2x + 12k2x Combine like terms: -48ikx + 48ikx = 0 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 0 + 60i2x + -60i2x + 24jkx + -24jkx + -12k2x + 12k2x 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 60i2x + -60i2x + 24jkx + -24jkx + -12k2x + 12k2x Combine like terms: 60i2x + -60i2x = 0 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 0 + 24jkx + -24jkx + -12k2x + 12k2x 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 24jkx + -24jkx + -12k2x + 12k2x Combine like terms: 24jkx + -24jkx = 0 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 0 + -12k2x + 12k2x 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = -12k2x + 12k2x Combine like terms: -12k2x + 12k2x = 0 24ijx + 48ikx + -60i2x + -24jkx + 12k2x = 0 Factor out the Greatest Common Factor (GCF), '12x'. 12x(2ij + 4ik + -5i2 + -2jk + k2) = 0 Ignore the factor 12.Subproblem 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 '(2ij + 4ik + -5i2 + -2jk + k2)' equal to zero and attempt to solve: Simplifying 2ij + 4ik + -5i2 + -2jk + k2 = 0 Solving 2ij + 4ik + -5i2 + -2jk + k2 = 0 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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