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Simplifying (45x + 75) = (3x + 5)(15x + 15) Reorder the terms: (75 + 45x) = (3x + 5)(15x + 15) Remove parenthesis around (75 + 45x) 75 + 45x = (3x + 5)(15x + 15) Reorder the terms: 75 + 45x = (5 + 3x)(15x + 15) Reorder the terms: 75 + 45x = (5 + 3x)(15 + 15x) Multiply (5 + 3x) * (15 + 15x) 75 + 45x = (5(15 + 15x) + 3x * (15 + 15x)) 75 + 45x = ((15 * 5 + 15x * 5) + 3x * (15 + 15x)) 75 + 45x = ((75 + 75x) + 3x * (15 + 15x)) 75 + 45x = (75 + 75x + (15 * 3x + 15x * 3x)) 75 + 45x = (75 + 75x + (45x + 45x2)) Combine like terms: 75x + 45x = 120x 75 + 45x = (75 + 120x + 45x2) Add '-75' to each side of the equation. 75 + -75 + 45x = 75 + 120x + -75 + 45x2 Combine like terms: 75 + -75 = 0 0 + 45x = 75 + 120x + -75 + 45x2 45x = 75 + 120x + -75 + 45x2 Reorder the terms: 45x = 75 + -75 + 120x + 45x2 Combine like terms: 75 + -75 = 0 45x = 0 + 120x + 45x2 45x = 120x + 45x2 Solving 45x = 120x + 45x2 Solving for variable 'x'. Combine like terms: 45x + -120x = -75x -75x + -45x2 = 120x + 45x2 + -120x + -45x2 Reorder the terms: -75x + -45x2 = 120x + -120x + 45x2 + -45x2 Combine like terms: 120x + -120x = 0 -75x + -45x2 = 0 + 45x2 + -45x2 -75x + -45x2 = 45x2 + -45x2 Combine like terms: 45x2 + -45x2 = 0 -75x + -45x2 = 0 Factor out the Greatest Common Factor (GCF), '-15x'. -15x(5 + 3x) = 0 Ignore the factor -15.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve: Simplifying 5 + 3x = 0 Solving 5 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3x = 0 + -5 3x = 0 + -5 Combine like terms: 0 + -5 = -5 3x = -5 Divide each side by '3'. x = -1.666666667 Simplifying x = -1.666666667Solution
x = {0, -1.666666667}
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