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Simplifying 5(3k + -4) + -3(k + -2) + -4(2k + -3) = 0 Reorder the terms: 5(-4 + 3k) + -3(k + -2) + -4(2k + -3) = 0 (-4 * 5 + 3k * 5) + -3(k + -2) + -4(2k + -3) = 0 (-20 + 15k) + -3(k + -2) + -4(2k + -3) = 0 Reorder the terms: -20 + 15k + -3(-2 + k) + -4(2k + -3) = 0 -20 + 15k + (-2 * -3 + k * -3) + -4(2k + -3) = 0 -20 + 15k + (6 + -3k) + -4(2k + -3) = 0 Reorder the terms: -20 + 15k + 6 + -3k + -4(-3 + 2k) = 0 -20 + 15k + 6 + -3k + (-3 * -4 + 2k * -4) = 0 -20 + 15k + 6 + -3k + (12 + -8k) = 0 Reorder the terms: -20 + 6 + 12 + 15k + -3k + -8k = 0 Combine like terms: -20 + 6 = -14 -14 + 12 + 15k + -3k + -8k = 0 Combine like terms: -14 + 12 = -2 -2 + 15k + -3k + -8k = 0 Combine like terms: 15k + -3k = 12k -2 + 12k + -8k = 0 Combine like terms: 12k + -8k = 4k -2 + 4k = 0 Solving -2 + 4k = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 4k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4k = 0 + 2 4k = 0 + 2 Combine like terms: 0 + 2 = 2 4k = 2 Divide each side by '4'. k = 0.5 Simplifying k = 0.5
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