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Simplifying (s + -1t)(2s + -3t) = 0 Multiply (s + -1t) * (2s + -3t) (s(2s + -3t) + -1t * (2s + -3t)) = 0 ((2s * s + -3t * s) + -1t * (2s + -3t)) = 0 Reorder the terms: ((-3st + 2s2) + -1t * (2s + -3t)) = 0 ((-3st + 2s2) + -1t * (2s + -3t)) = 0 (-3st + 2s2 + (2s * -1t + -3t * -1t)) = 0 (-3st + 2s2 + (-2st + 3t2)) = 0 Reorder the terms: (-3st + -2st + 2s2 + 3t2) = 0 Combine like terms: -3st + -2st = -5st (-5st + 2s2 + 3t2) = 0 Solving -5st + 2s2 + 3t2 = 0 Solving for variable 's'. Factor a trinomial. (2s + -3t)(s + -1t) = 0Subproblem 1
Set the factor '(2s + -3t)' equal to zero and attempt to solve: Simplifying 2s + -3t = 0 Solving 2s + -3t = 0 Move all terms containing s to the left, all other terms to the right. Add '3t' to each side of the equation. 2s + -3t + 3t = 0 + 3t Combine like terms: -3t + 3t = 0 2s + 0 = 0 + 3t 2s = 0 + 3t Remove the zero: 2s = 3t Divide each side by '2'. s = 1.5t Simplifying s = 1.5tSubproblem 2
Set the factor '(s + -1t)' equal to zero and attempt to solve: Simplifying s + -1t = 0 Solving s + -1t = 0 Move all terms containing s to the left, all other terms to the right. Add 't' to each side of the equation. s + -1t + t = 0 + t Combine like terms: -1t + t = 0 s + 0 = 0 + t s = 0 + t Remove the zero: s = t Simplifying s = tSolution
s = {1.5t, t}
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