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Simplifying (3x + 2)(x + 5) = 10 Reorder the terms: (2 + 3x)(x + 5) = 10 Reorder the terms: (2 + 3x)(5 + x) = 10 Multiply (2 + 3x) * (5 + x) (2(5 + x) + 3x * (5 + x)) = 10 ((5 * 2 + x * 2) + 3x * (5 + x)) = 10 ((10 + 2x) + 3x * (5 + x)) = 10 (10 + 2x + (5 * 3x + x * 3x)) = 10 (10 + 2x + (15x + 3x2)) = 10 Combine like terms: 2x + 15x = 17x (10 + 17x + 3x2) = 10 Add '-10' to each side of the equation. 10 + 17x + -10 + 3x2 = 10 + -10 Reorder the terms: 10 + -10 + 17x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 0 + 17x + 3x2 = 10 + -10 17x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 17x + 3x2 = 0 Solving 17x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(17 + 3x) = 0Subproblem 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 '(17 + 3x)' equal to zero and attempt to solve: Simplifying 17 + 3x = 0 Solving 17 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + 3x = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 3x = 0 + -17 3x = 0 + -17 Combine like terms: 0 + -17 = -17 3x = -17 Divide each side by '3'. x = -5.666666667 Simplifying x = -5.666666667Solution
x = {0, -5.666666667}
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