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Simplifying 6st4 + 18st2 + -168s = 0 Reorder the terms: -168s + 18st2 + 6st4 = 0 Solving -168s + 18st2 + 6st4 = 0 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '6s'. 6s(-28 + 3t2 + t4) = 0 Factor a trinomial. 6s((-7 + -1t2)(4 + -1t2)) = 0 Factor a difference between two squares. 6s((-7 + -1t2)((2 + t)(2 + -1t))) = 0 Ignore the factor 6.Subproblem 1
Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s = 0Subproblem 2
Set the factor '(-7 + -1t2)' equal to zero and attempt to solve: Simplifying -7 + -1t2 = 0 Solving -7 + -1t2 = 0 Move all terms containing s to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1t2 = 0 + 7 -1t2 = 0 + 7 Combine like terms: 0 + 7 = 7 -1t2 = 7 Add 't2' to each side of the equation. -1t2 + t2 = 7 + t2 Combine like terms: -1t2 + t2 = 0 0 = 7 + t2 Simplifying 0 = 7 + t2 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 '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Add '-1t' to each side of the equation. t + -1t = -2 + -1t Combine like terms: t + -1t = 0 0 = -2 + -1t Simplifying 0 = -2 + -1t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Add 't' to each side of the equation. -1t + t = -2 + t Combine like terms: -1t + t = 0 0 = -2 + t Simplifying 0 = -2 + t The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
s = {0}
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