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Simplifying k * x2 = 5k * x + 6k Multiply k * x2 kx2 = 5k * x + 6k Multiply k * x kx2 = 5kx + 6k Reorder the terms: kx2 = 6k + 5kx Solving kx2 = 6k + 5kx Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-6k' to each side of the equation. -6k + kx2 = 6k + -6k + 5kx Combine like terms: 6k + -6k = 0 -6k + kx2 = 0 + 5kx -6k + kx2 = 5kx Add '-5kx' to each side of the equation. -6k + -5kx + kx2 = 5kx + -5kx Combine like terms: 5kx + -5kx = 0 -6k + -5kx + kx2 = 0 Factor out the Greatest Common Factor (GCF), 'k'. k(-6 + -5x + x2) = 0 Factor a trinomial. k((-1 + -1x)(6 + -1x)) = 0Subproblem 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 '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Add 'x' to each side of the equation. -1x + x = 1 + x Combine like terms: -1x + x = 0 0 = 1 + x Simplifying 0 = 1 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing k to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Add 'x' to each side of the equation. -1x + x = -6 + x Combine like terms: -1x + x = 0 0 = -6 + x Simplifying 0 = -6 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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