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Simplifying 4t(-1i + 3) + -3(6 + -2i) = 0 Reorder the terms: 4t(3 + -1i) + -3(6 + -2i) = 0 (3 * 4t + -1i * 4t) + -3(6 + -2i) = 0 Reorder the terms: (-4it + 12t) + -3(6 + -2i) = 0 (-4it + 12t) + -3(6 + -2i) = 0 -4it + 12t + (6 * -3 + -2i * -3) = 0 -4it + 12t + (-18 + 6i) = 0 Reorder the terms: -18 + 6i + -4it + 12t = 0 Solving -18 + 6i + -4it + 12t = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 6i + -4it + 18 + 12t = 0 + 18 Reorder the terms: -18 + 18 + 6i + -4it + 12t = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 6i + -4it + 12t = 0 + 18 6i + -4it + 12t = 0 + 18 Combine like terms: 0 + 18 = 18 6i + -4it + 12t = 18 Add '-12t' to each side of the equation. 6i + -4it + 12t + -12t = 18 + -12t Combine like terms: 12t + -12t = 0 6i + -4it + 0 = 18 + -12t 6i + -4it = 18 + -12t Reorder the terms: -18 + 6i + -4it + 12t = 18 + -12t + -18 + 12t Reorder the terms: -18 + 6i + -4it + 12t = 18 + -18 + -12t + 12t Combine like terms: 18 + -18 = 0 -18 + 6i + -4it + 12t = 0 + -12t + 12t -18 + 6i + -4it + 12t = -12t + 12t Combine like terms: -12t + 12t = 0 -18 + 6i + -4it + 12t = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 3i + -2it + 6t) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 3i + -2it + 6t)' equal to zero and attempt to solve: Simplifying -9 + 3i + -2it + 6t = 0 Solving -9 + 3i + -2it + 6t = 0 Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 3i + -2it + 9 + 6t = 0 + 9 Reorder the terms: -9 + 9 + 3i + -2it + 6t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3i + -2it + 6t = 0 + 9 3i + -2it + 6t = 0 + 9 Combine like terms: 0 + 9 = 9 3i + -2it + 6t = 9 Add '-6t' to each side of the equation. 3i + -2it + 6t + -6t = 9 + -6t Combine like terms: 6t + -6t = 0 3i + -2it + 0 = 9 + -6t 3i + -2it = 9 + -6t 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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