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Simplifying 3(4j + 2) + -5(2j + -6) + 4(6J + -1) = 0 Reorder the terms: 3(2 + 4j) + -5(2j + -6) + 4(6J + -1) = 0 (2 * 3 + 4j * 3) + -5(2j + -6) + 4(6J + -1) = 0 (6 + 12j) + -5(2j + -6) + 4(6J + -1) = 0 Reorder the terms: 6 + 12j + -5(-6 + 2j) + 4(6J + -1) = 0 6 + 12j + (-6 * -5 + 2j * -5) + 4(6J + -1) = 0 6 + 12j + (30 + -10j) + 4(6J + -1) = 0 Reorder the terms: 6 + 12j + 30 + -10j + 4(-1 + 6J) = 0 6 + 12j + 30 + -10j + (-1 * 4 + 6J * 4) = 0 6 + 12j + 30 + -10j + (-4 + 24J) = 0 Reorder the terms: 6 + 30 + -4 + 24J + 12j + -10j = 0 Combine like terms: 6 + 30 = 36 36 + -4 + 24J + 12j + -10j = 0 Combine like terms: 36 + -4 = 32 32 + 24J + 12j + -10j = 0 Combine like terms: 12j + -10j = 2j 32 + 24J + 2j = 0 Solving 32 + 24J + 2j = 0 Solving for variable 'J'. Move all terms containing J to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + 24J + -32 + 2j = 0 + -32 Reorder the terms: 32 + -32 + 24J + 2j = 0 + -32 Combine like terms: 32 + -32 = 0 0 + 24J + 2j = 0 + -32 24J + 2j = 0 + -32 Combine like terms: 0 + -32 = -32 24J + 2j = -32 Add '-2j' to each side of the equation. 24J + 2j + -2j = -32 + -2j Combine like terms: 2j + -2j = 0 24J + 0 = -32 + -2j 24J = -32 + -2j Divide each side by '24'. J = -1.333333333 + -0.08333333333j Simplifying J = -1.333333333 + -0.08333333333j
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