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Simplifying (r + -3) * 40 + (r + 3) * 40 = 14(r + 3)(r + -3) Reorder the terms: (-3 + r) * 40 + (r + 3) * 40 = 14(r + 3)(r + -3) Reorder the terms for easier multiplication: 40(-3 + r) + (r + 3) * 40 = 14(r + 3)(r + -3) (-3 * 40 + r * 40) + (r + 3) * 40 = 14(r + 3)(r + -3) (-120 + 40r) + (r + 3) * 40 = 14(r + 3)(r + -3) Reorder the terms: -120 + 40r + (3 + r) * 40 = 14(r + 3)(r + -3) Reorder the terms for easier multiplication: -120 + 40r + 40(3 + r) = 14(r + 3)(r + -3) -120 + 40r + (3 * 40 + r * 40) = 14(r + 3)(r + -3) -120 + 40r + (120 + 40r) = 14(r + 3)(r + -3) Reorder the terms: -120 + 120 + 40r + 40r = 14(r + 3)(r + -3) Combine like terms: -120 + 120 = 0 0 + 40r + 40r = 14(r + 3)(r + -3) 40r + 40r = 14(r + 3)(r + -3) Combine like terms: 40r + 40r = 80r 80r = 14(r + 3)(r + -3) Reorder the terms: 80r = 14(3 + r)(r + -3) Reorder the terms: 80r = 14(3 + r)(-3 + r) Multiply (3 + r) * (-3 + r) 80r = 14(3(-3 + r) + r(-3 + r)) 80r = 14((-3 * 3 + r * 3) + r(-3 + r)) 80r = 14((-9 + 3r) + r(-3 + r)) 80r = 14(-9 + 3r + (-3 * r + r * r)) 80r = 14(-9 + 3r + (-3r + r2)) Combine like terms: 3r + -3r = 0 80r = 14(-9 + 0 + r2) 80r = 14(-9 + r2) 80r = (-9 * 14 + r2 * 14) 80r = (-126 + 14r2) Solving 80r = -126 + 14r2 Solving for variable 'r'. Reorder the terms: 126 + 80r + -14r2 = -126 + 14r2 + 126 + -14r2 Reorder the terms: 126 + 80r + -14r2 = -126 + 126 + 14r2 + -14r2 Combine like terms: -126 + 126 = 0 126 + 80r + -14r2 = 0 + 14r2 + -14r2 126 + 80r + -14r2 = 14r2 + -14r2 Combine like terms: 14r2 + -14r2 = 0 126 + 80r + -14r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(63 + 40r + -7r2) = 0 Factor a trinomial. 2((7 + -1r)(9 + 7r)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -1r)' equal to zero and attempt to solve: Simplifying 7 + -1r = 0 Solving 7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1r = 0 + -7 -1r = 0 + -7 Combine like terms: 0 + -7 = -7 -1r = -7 Divide each side by '-1'. r = 7 Simplifying r = 7Subproblem 2
Set the factor '(9 + 7r)' equal to zero and attempt to solve: Simplifying 9 + 7r = 0 Solving 9 + 7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 7r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7r = 0 + -9 7r = 0 + -9 Combine like terms: 0 + -9 = -9 7r = -9 Divide each side by '7'. r = -1.285714286 Simplifying r = -1.285714286Solution
r = {7, -1.285714286}
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