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