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Simplifying (2x + -3)(x + 12) = 2x2 + kx + -36 Reorder the terms: (-3 + 2x)(x + 12) = 2x2 + kx + -36 Reorder the terms: (-3 + 2x)(12 + x) = 2x2 + kx + -36 Multiply (-3 + 2x) * (12 + x) (-3(12 + x) + 2x * (12 + x)) = 2x2 + kx + -36 ((12 * -3 + x * -3) + 2x * (12 + x)) = 2x2 + kx + -36 ((-36 + -3x) + 2x * (12 + x)) = 2x2 + kx + -36 (-36 + -3x + (12 * 2x + x * 2x)) = 2x2 + kx + -36 (-36 + -3x + (24x + 2x2)) = 2x2 + kx + -36 Combine like terms: -3x + 24x = 21x (-36 + 21x + 2x2) = 2x2 + kx + -36 Reorder the terms: -36 + 21x + 2x2 = -36 + kx + 2x2 Add '36' to each side of the equation. -36 + 21x + 36 + 2x2 = -36 + kx + 36 + 2x2 Reorder the terms: -36 + 36 + 21x + 2x2 = -36 + kx + 36 + 2x2 Combine like terms: -36 + 36 = 0 0 + 21x + 2x2 = -36 + kx + 36 + 2x2 21x + 2x2 = -36 + kx + 36 + 2x2 Reorder the terms: 21x + 2x2 = -36 + 36 + kx + 2x2 Combine like terms: -36 + 36 = 0 21x + 2x2 = 0 + kx + 2x2 21x + 2x2 = kx + 2x2 Add '-2x2' to each side of the equation. 21x + 2x2 + -2x2 = kx + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 21x + 0 = kx + 2x2 + -2x2 21x = kx + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 21x = kx + 0 21x = kx Solving 21x = kx Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1kx' to each side of the equation. -1kx + 21x = kx + -1kx Combine like terms: kx + -1kx = 0 -1kx + 21x = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-1k + 21) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1k + 21)' equal to zero and attempt to solve: Simplifying -1k + 21 = 0 Reorder the terms: 21 + -1k = 0 Solving 21 + -1k = 0 Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1k = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1k = 0 + -21 -1k = 0 + -21 Combine like terms: 0 + -21 = -21 -1k = -21 Add 'k' to each side of the equation. -1k + k = -21 + k Combine like terms: -1k + k = 0 0 = -21 + k Simplifying 0 = -21 + k The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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