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Simplifying 8[2k + -1(3m + 5)] + 2[9k + -1(4m + -7)] = 0 Reorder the terms: 8[2k + -1(5 + 3m)] + 2[9k + -1(4m + -7)] = 0 8[2k + (5 * -1 + 3m * -1)] + 2[9k + -1(4m + -7)] = 0 8[2k + (-5 + -3m)] + 2[9k + -1(4m + -7)] = 0 Reorder the terms: 8[-5 + 2k + -3m] + 2[9k + -1(4m + -7)] = 0 [-5 * 8 + 2k * 8 + -3m * 8] + 2[9k + -1(4m + -7)] = 0 [-40 + 16k + -24m] + 2[9k + -1(4m + -7)] = 0 Reorder the terms: -40 + 16k + -24m + 2[9k + -1(-7 + 4m)] = 0 -40 + 16k + -24m + 2[9k + (-7 * -1 + 4m * -1)] = 0 -40 + 16k + -24m + 2[9k + (7 + -4m)] = 0 Reorder the terms: -40 + 16k + -24m + 2[7 + 9k + -4m] = 0 -40 + 16k + -24m + [7 * 2 + 9k * 2 + -4m * 2] = 0 -40 + 16k + -24m + [14 + 18k + -8m] = 0 Reorder the terms: -40 + 14 + 16k + 18k + -24m + -8m = 0 Combine like terms: -40 + 14 = -26 -26 + 16k + 18k + -24m + -8m = 0 Combine like terms: 16k + 18k = 34k -26 + 34k + -24m + -8m = 0 Combine like terms: -24m + -8m = -32m -26 + 34k + -32m = 0 Solving -26 + 34k + -32m = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 34k + 26 + -32m = 0 + 26 Reorder the terms: -26 + 26 + 34k + -32m = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 34k + -32m = 0 + 26 34k + -32m = 0 + 26 Combine like terms: 0 + 26 = 26 34k + -32m = 26 Add '32m' to each side of the equation. 34k + -32m + 32m = 26 + 32m Combine like terms: -32m + 32m = 0 34k + 0 = 26 + 32m 34k = 26 + 32m Divide each side by '34'. k = 0.7647058824 + 0.9411764706m Simplifying k = 0.7647058824 + 0.9411764706m
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