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Simplifying 6x + 15i = 12 + 3yi Reorder the terms: 15i + 6x = 12 + 3yi Solving 15i + 6x = 12 + 3iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3iy' to each side of the equation. 15i + -3iy + 6x = 12 + 3iy + -3iy Combine like terms: 3iy + -3iy = 0 15i + -3iy + 6x = 12 + 0 15i + -3iy + 6x = 12 Add '-6x' to each side of the equation. 15i + -3iy + 6x + -6x = 12 + -6x Combine like terms: 6x + -6x = 0 15i + -3iy + 0 = 12 + -6x 15i + -3iy = 12 + -6x Reorder the terms: -12 + 15i + -3iy + 6x = 12 + -6x + -12 + 6x Reorder the terms: -12 + 15i + -3iy + 6x = 12 + -12 + -6x + 6x Combine like terms: 12 + -12 = 0 -12 + 15i + -3iy + 6x = 0 + -6x + 6x -12 + 15i + -3iy + 6x = -6x + 6x Combine like terms: -6x + 6x = 0 -12 + 15i + -3iy + 6x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 5i + -1iy + 2x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 5i + -1iy + 2x)' equal to zero and attempt to solve: Simplifying -4 + 5i + -1iy + 2x = 0 Solving -4 + 5i + -1iy + 2x = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 5i + -1iy + 4 + 2x = 0 + 4 Reorder the terms: -4 + 4 + 5i + -1iy + 2x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 5i + -1iy + 2x = 0 + 4 5i + -1iy + 2x = 0 + 4 Combine like terms: 0 + 4 = 4 5i + -1iy + 2x = 4 Add '-2x' to each side of the equation. 5i + -1iy + 2x + -2x = 4 + -2x Combine like terms: 2x + -2x = 0 5i + -1iy + 0 = 4 + -2x 5i + -1iy = 4 + -2x 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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