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Simplifying (5h + -3j + 8k) + -3(-5h + 5j + -5k) = 0 Remove parenthesis around (5h + -3j + 8k) 5h + -3j + 8k + -3(-5h + 5j + -5k) = 0 5h + -3j + 8k + (-5h * -3 + 5j * -3 + -5k * -3) = 0 5h + -3j + 8k + (15h + -15j + 15k) = 0 Reorder the terms: 5h + 15h + -3j + -15j + 8k + 15k = 0 Combine like terms: 5h + 15h = 20h 20h + -3j + -15j + 8k + 15k = 0 Combine like terms: -3j + -15j = -18j 20h + -18j + 8k + 15k = 0 Combine like terms: 8k + 15k = 23k 20h + -18j + 23k = 0 Solving 20h + -18j + 23k = 0 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '18j' to each side of the equation. 20h + -18j + 18j + 23k = 0 + 18j Combine like terms: -18j + 18j = 0 20h + 0 + 23k = 0 + 18j 20h + 23k = 0 + 18j Remove the zero: 20h + 23k = 18j Add '-23k' to each side of the equation. 20h + 23k + -23k = 18j + -23k Combine like terms: 23k + -23k = 0 20h + 0 = 18j + -23k 20h = 18j + -23k Divide each side by '20'. h = 0.9j + -1.15k Simplifying h = 0.9j + -1.15k
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