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Simplifying 12(s + 7)(5s + -15) = 0 Reorder the terms: 12(7 + s)(5s + -15) = 0 Reorder the terms: 12(7 + s)(-15 + 5s) = 0 Multiply (7 + s) * (-15 + 5s) 12(7(-15 + 5s) + s(-15 + 5s)) = 0 12((-15 * 7 + 5s * 7) + s(-15 + 5s)) = 0 12((-105 + 35s) + s(-15 + 5s)) = 0 12(-105 + 35s + (-15 * s + 5s * s)) = 0 12(-105 + 35s + (-15s + 5s2)) = 0 Combine like terms: 35s + -15s = 20s 12(-105 + 20s + 5s2) = 0 (-105 * 12 + 20s * 12 + 5s2 * 12) = 0 (-1260 + 240s + 60s2) = 0 Solving -1260 + 240s + 60s2 = 0 Solving for variable 's'. Factor out the Greatest Common Factor (GCF), '60'. 60(-21 + 4s + s2) = 0 Factor a trinomial. 60((-7 + -1s)(3 + -1s)) = 0 Ignore the factor 60.Subproblem 1
Set the factor '(-7 + -1s)' equal to zero and attempt to solve: Simplifying -7 + -1s = 0 Solving -7 + -1s = 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 + -1s = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1s = 0 + 7 -1s = 0 + 7 Combine like terms: 0 + 7 = 7 -1s = 7 Divide each side by '-1'. s = -7 Simplifying s = -7Subproblem 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 = {-7, 3}
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