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Simplifying (5s + 7)(s + 5) = 23 Reorder the terms: (7 + 5s)(s + 5) = 23 Reorder the terms: (7 + 5s)(5 + s) = 23 Multiply (7 + 5s) * (5 + s) (7(5 + s) + 5s * (5 + s)) = 23 ((5 * 7 + s * 7) + 5s * (5 + s)) = 23 ((35 + 7s) + 5s * (5 + s)) = 23 (35 + 7s + (5 * 5s + s * 5s)) = 23 (35 + 7s + (25s + 5s2)) = 23 Combine like terms: 7s + 25s = 32s (35 + 32s + 5s2) = 23 Solving 35 + 32s + 5s2 = 23 Solving for variable 's'. Reorder the terms: 35 + -23 + 32s + 5s2 = 23 + -23 Combine like terms: 35 + -23 = 12 12 + 32s + 5s2 = 23 + -23 Combine like terms: 23 + -23 = 0 12 + 32s + 5s2 = 0 Factor a trinomial. (6 + s)(2 + 5s) = 0Subproblem 1
Set the factor '(6 + s)' equal to zero and attempt to solve: Simplifying 6 + s = 0 Solving 6 + s = 0 Move all terms containing s to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + s = 0 + -6 Combine like terms: 6 + -6 = 0 0 + s = 0 + -6 s = 0 + -6 Combine like terms: 0 + -6 = -6 s = -6 Simplifying s = -6Subproblem 2
Set the factor '(2 + 5s)' equal to zero and attempt to solve: Simplifying 2 + 5s = 0 Solving 2 + 5s = 0 Move all terms containing s to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 5s = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5s = 0 + -2 5s = 0 + -2 Combine like terms: 0 + -2 = -2 5s = -2 Divide each side by '5'. s = -0.4 Simplifying s = -0.4Solution
s = {-6, -0.4}
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