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Simplifying 180s3 + 15s2t3 + -240s2t2 = 0 Reorder the terms: -240s2t2 + 15s2t3 + 180s3 = 0 Solving -240s2t2 + 15s2t3 + 180s3 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '15s2'. 15s2(-16t2 + t3 + 12s) = 0 Ignore the factor 15.Subproblem 1
Set the factor 's2' equal to zero and attempt to solve: Simplifying s2 = 0 Solving s2 = 0 Move all terms containing s to the left, all other terms to the right. Simplifying s2 = 0 Take the square root of each side: s = {0}Subproblem 2
Set the factor '(-16t2 + t3 + 12s)' equal to zero and attempt to solve: Simplifying -16t2 + t3 + 12s = 0 Reorder the terms: 12s + -16t2 + t3 = 0 Solving 12s + -16t2 + t3 = 0 Move all terms containing s to the left, all other terms to the right. Add '16t2' to each side of the equation. 12s + -16t2 + 16t2 + t3 = 0 + 16t2 Combine like terms: -16t2 + 16t2 = 0 12s + 0 + t3 = 0 + 16t2 12s + t3 = 0 + 16t2 Remove the zero: 12s + t3 = 16t2 Add '-1t3' to each side of the equation. 12s + t3 + -1t3 = 16t2 + -1t3 Combine like terms: t3 + -1t3 = 0 12s + 0 = 16t2 + -1t3 12s = 16t2 + -1t3 Divide each side by '12'. s = 1.333333333t2 + -0.08333333333t3 Simplifying s = 1.333333333t2 + -0.08333333333t3Solution
s = {0, 1.333333333t2 + -0.08333333333t3}
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