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Simplifying k(x2 + -5k + 6) + (3x2 + -7x + 3) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms: k(6 + -5k + x2) + (3x2 + -7x + 3) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) (6 * k + -5k * k + x2 * k) + (3x2 + -7x + 3) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms: (6k + kx2 + -5k2) + (3x2 + -7x + 3) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) (6k + kx2 + -5k2) + (3x2 + -7x + 3) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms: 6k + kx2 + -5k2 + (3 + -7x + 3x2) = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Remove parenthesis around (3 + -7x + 3x2) 6k + kx2 + -5k2 + 3 + -7x + 3x2 = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = (k + 3) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = (3 + k) * x2 + -1(5k + 7) * x + (6k + 3) Reorder the terms for easier multiplication: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = x2(3 + k) + -1(5k + 7) * x + (6k + 3) 3 + 6k + kx2 + -5k2 + -7x + 3x2 = (3 * x2 + k * x2) + -1(5k + 7) * x + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = (kx2 + 3x2) + -1(5k + 7) * x + (6k + 3) 3 + 6k + kx2 + -5k2 + -7x + 3x2 = (kx2 + 3x2) + -1(5k + 7) * x + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + -1(7 + 5k) * x + (6k + 3) Reorder the terms for easier multiplication: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + -1x(7 + 5k) + (6k + 3) 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + (7 * -1x + 5k * -1x) + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + (-5kx + -7x) + (6k + 3) 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + (-5kx + -7x) + (6k + 3) Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + -5kx + -7x + (3 + 6k) Remove parenthesis around (3 + 6k) 3 + 6k + kx2 + -5k2 + -7x + 3x2 = kx2 + 3x2 + -5kx + -7x + 3 + 6k Reorder the terms: 3 + 6k + kx2 + -5k2 + -7x + 3x2 = 3 + 6k + -5kx + kx2 + -7x + 3x2 Add '-3' to each side of the equation. 3 + 6k + kx2 + -5k2 + -7x + -3 + 3x2 = 3 + 6k + -5kx + kx2 + -7x + -3 + 3x2 Reorder the terms: 3 + -3 + 6k + kx2 + -5k2 + -7x + 3x2 = 3 + 6k + -5kx + kx2 + -7x + -3 + 3x2 Combine like terms: 3 + -3 = 0 0 + 6k + kx2 + -5k2 + -7x + 3x2 = 3 + 6k + -5kx + kx2 + -7x + -3 + 3x2 6k + kx2 + -5k2 + -7x + 3x2 = 3 + 6k + -5kx + kx2 + -7x + -3 + 3x2 Reorder the terms: 6k + kx2 + -5k2 + -7x + 3x2 = 3 + -3 + 6k + -5kx + kx2 + -7x + 3x2 Combine like terms: 3 + -3 = 0 6k + kx2 + -5k2 + -7x + 3x2 = 0 + 6k + -5kx + kx2 + -7x + 3x2 6k + kx2 + -5k2 + -7x + 3x2 = 6k + -5kx + kx2 + -7x + 3x2 Add '-6k' to each side of the equation. 6k + kx2 + -5k2 + -7x + -6k + 3x2 = 6k + -5kx + kx2 + -7x + -6k + 3x2 Reorder the terms: 6k + -6k + kx2 + -5k2 + -7x + 3x2 = 6k + -5kx + kx2 + -7x + -6k + 3x2 Combine like terms: 6k + -6k = 0 0 + kx2 + -5k2 + -7x + 3x2 = 6k + -5kx + kx2 + -7x + -6k + 3x2 kx2 + -5k2 + -7x + 3x2 = 6k + -5kx + kx2 + -7x + -6k + 3x2 Reorder the terms: kx2 + -5k2 + -7x + 3x2 = 6k + -6k + -5kx + kx2 + -7x + 3x2 Combine like terms: 6k + -6k = 0 kx2 + -5k2 + -7x + 3x2 = 0 + -5kx + kx2 + -7x + 3x2 kx2 + -5k2 + -7x + 3x2 = -5kx + kx2 + -7x + 3x2 Add '-1kx2' to each side of the equation. kx2 + -5k2 + -7x + -1kx2 + 3x2 = -5kx + kx2 + -7x + -1kx2 + 3x2 Reorder the terms: kx2 + -1kx2 + -5k2 + -7x + 3x2 = -5kx + kx2 + -7x + -1kx2 + 3x2 Combine like terms: kx2 + -1kx2 = 0 0 + -5k2 + -7x + 3x2 = -5kx + kx2 + -7x + -1kx2 + 3x2 -5k2 + -7x + 3x2 = -5kx + kx2 + -7x + -1kx2 + 3x2 Reorder the terms: -5k2 + -7x + 3x2 = -5kx + kx2 + -1kx2 + -7x + 3x2 Combine like terms: kx2 + -1kx2 = 0 -5k2 + -7x + 3x2 = -5kx + 0 + -7x + 3x2 -5k2 + -7x + 3x2 = -5kx + -7x + 3x2 Add '7x' to each side of the equation. -5k2 + -7x + 7x + 3x2 = -5kx + -7x + 7x + 3x2 Combine like terms: -7x + 7x = 0 -5k2 + 0 + 3x2 = -5kx + -7x + 7x + 3x2 -5k2 + 3x2 = -5kx + -7x + 7x + 3x2 Combine like terms: -7x + 7x = 0 -5k2 + 3x2 = -5kx + 0 + 3x2 -5k2 + 3x2 = -5kx + 3x2 Add '-3x2' to each side of the equation. -5k2 + 3x2 + -3x2 = -5kx + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -5k2 + 0 = -5kx + 3x2 + -3x2 -5k2 = -5kx + 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -5k2 = -5kx + 0 -5k2 = -5kx Solving -5k2 = -5kx Solving for variable 'k'. Reorder the terms: 5kx + -5k2 = -5kx + 5kx Combine like terms: -5kx + 5kx = 0 5kx + -5k2 = 0 Factor out the Greatest Common Factor (GCF), '5k'. 5k(x + -1k) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(x + -1k)' equal to zero and attempt to solve: Simplifying x + -1k = 0 Reorder the terms: -1k + x = 0 Solving -1k + x = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. -1k + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 -1k + 0 = 0 + -1x -1k = 0 + -1x Remove the zero: -1k = -1x Divide each side by '-1'. k = x Simplifying k = xSolution
k = {0, x}
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