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Simplifying 9x3 + 6kx2 + (1 + -3k) * x = 0 Reorder the terms for easier multiplication: 9x3 + 6kx2 + x(1 + -3k) = 0 9x3 + 6kx2 + (1 * x + -3k * x) = 0 Reorder the terms: 9x3 + 6kx2 + (-3kx + 1x) = 0 9x3 + 6kx2 + (-3kx + 1x) = 0 Reorder the terms: -3kx + 6kx2 + 1x + 9x3 = 0 Solving -3kx + 6kx2 + 1x + 9x3 = 0 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. -3kx + 6kx2 + 1x + -1x + 9x3 = 0 + -1x Combine like terms: 1x + -1x = 0 -3kx + 6kx2 + 0 + 9x3 = 0 + -1x -3kx + 6kx2 + 9x3 = 0 + -1x Remove the zero: -3kx + 6kx2 + 9x3 = -1x Add '-9x3' to each side of the equation. -3kx + 6kx2 + 9x3 + -9x3 = -1x + -9x3 Combine like terms: 9x3 + -9x3 = 0 -3kx + 6kx2 + 0 = -1x + -9x3 -3kx + 6kx2 = -1x + -9x3 Reorder the terms: -3kx + 6kx2 + x + 9x3 = -1x + x + -9x3 + 9x3 Combine like terms: -1x + x = 0 -3kx + 6kx2 + x + 9x3 = 0 + -9x3 + 9x3 -3kx + 6kx2 + x + 9x3 = -9x3 + 9x3 Combine like terms: -9x3 + 9x3 = 0 -3kx + 6kx2 + x + 9x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-3k + 6kx + 1 + 9x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing k to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3k + 6kx + 1 + 9x2)' equal to zero and attempt to solve: Simplifying -3k + 6kx + 1 + 9x2 = 0 Reorder the terms: 1 + -3k + 6kx + 9x2 = 0 Solving 1 + -3k + 6kx + 9x2 = 0 Move all terms containing k to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -3k + 6kx + -1 + 9x2 = 0 + -1 Reorder the terms: 1 + -1 + -3k + 6kx + 9x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3k + 6kx + 9x2 = 0 + -1 -3k + 6kx + 9x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -3k + 6kx + 9x2 = -1 Add '-9x2' to each side of the equation. -3k + 6kx + 9x2 + -9x2 = -1 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -3k + 6kx + 0 = -1 + -9x2 -3k + 6kx = -1 + -9x2 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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