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Simplifying (s + 5)(6s + -7) = 0 Reorder the terms: (5 + s)(6s + -7) = 0 Reorder the terms: (5 + s)(-7 + 6s) = 0 Multiply (5 + s) * (-7 + 6s) (5(-7 + 6s) + s(-7 + 6s)) = 0 ((-7 * 5 + 6s * 5) + s(-7 + 6s)) = 0 ((-35 + 30s) + s(-7 + 6s)) = 0 (-35 + 30s + (-7 * s + 6s * s)) = 0 (-35 + 30s + (-7s + 6s2)) = 0 Combine like terms: 30s + -7s = 23s (-35 + 23s + 6s2) = 0 Solving -35 + 23s + 6s2 = 0 Solving for variable 's'. Factor a trinomial. (-5 + -1s)(7 + -6s) = 0Subproblem 1
Set the factor '(-5 + -1s)' equal to zero and attempt to solve: Simplifying -5 + -1s = 0 Solving -5 + -1s = 0 Move all terms containing s to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1s = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1s = 0 + 5 -1s = 0 + 5 Combine like terms: 0 + 5 = 5 -1s = 5 Divide each side by '-1'. s = -5 Simplifying s = -5Subproblem 2
Set the factor '(7 + -6s)' equal to zero and attempt to solve: Simplifying 7 + -6s = 0 Solving 7 + -6s = 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 + -6s = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6s = 0 + -7 -6s = 0 + -7 Combine like terms: 0 + -7 = -7 -6s = -7 Divide each side by '-6'. s = 1.166666667 Simplifying s = 1.166666667Solution
s = {-5, 1.166666667}
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