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Simplifying (3s + 1)(s + -4) = -5(s + -1) Reorder the terms: (1 + 3s)(s + -4) = -5(s + -1) Reorder the terms: (1 + 3s)(-4 + s) = -5(s + -1) Multiply (1 + 3s) * (-4 + s) (1(-4 + s) + 3s * (-4 + s)) = -5(s + -1) ((-4 * 1 + s * 1) + 3s * (-4 + s)) = -5(s + -1) ((-4 + 1s) + 3s * (-4 + s)) = -5(s + -1) (-4 + 1s + (-4 * 3s + s * 3s)) = -5(s + -1) (-4 + 1s + (-12s + 3s2)) = -5(s + -1) Combine like terms: 1s + -12s = -11s (-4 + -11s + 3s2) = -5(s + -1) Reorder the terms: -4 + -11s + 3s2 = -5(-1 + s) -4 + -11s + 3s2 = (-1 * -5 + s * -5) -4 + -11s + 3s2 = (5 + -5s) Solving -4 + -11s + 3s2 = 5 + -5s Solving for variable 's'. Reorder the terms: -4 + -5 + -11s + 5s + 3s2 = 5 + -5s + -5 + 5s Combine like terms: -4 + -5 = -9 -9 + -11s + 5s + 3s2 = 5 + -5s + -5 + 5s Combine like terms: -11s + 5s = -6s -9 + -6s + 3s2 = 5 + -5s + -5 + 5s Reorder the terms: -9 + -6s + 3s2 = 5 + -5 + -5s + 5s Combine like terms: 5 + -5 = 0 -9 + -6s + 3s2 = 0 + -5s + 5s -9 + -6s + 3s2 = -5s + 5s Combine like terms: -5s + 5s = 0 -9 + -6s + 3s2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-3 + -2s + s2) = 0 Factor a trinomial. 3((-1 + -1s)(3 + -1s)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -1s)' equal to zero and attempt to solve: Simplifying -1 + -1s = 0 Solving -1 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1s = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1s = 0 + 1 -1s = 0 + 1 Combine like terms: 0 + 1 = 1 -1s = 1 Divide each side by '-1'. s = -1 Simplifying s = -1Subproblem 2
Set the factor '(3 + -1s)' equal to zero and attempt to solve: Simplifying 3 + -1s = 0 Solving 3 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1s = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1s = 0 + -3 -1s = 0 + -3 Combine like terms: 0 + -3 = -3 -1s = -3 Divide each side by '-1'. s = 3 Simplifying s = 3Solution
s = {-1, 3}
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