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Simplifying (2x + 10)(3x + 5) = 0 Reorder the terms: (10 + 2x)(3x + 5) = 0 Reorder the terms: (10 + 2x)(5 + 3x) = 0 Multiply (10 + 2x) * (5 + 3x) (10(5 + 3x) + 2x * (5 + 3x)) = 0 ((5 * 10 + 3x * 10) + 2x * (5 + 3x)) = 0 ((50 + 30x) + 2x * (5 + 3x)) = 0 (50 + 30x + (5 * 2x + 3x * 2x)) = 0 (50 + 30x + (10x + 6x2)) = 0 Combine like terms: 30x + 10x = 40x (50 + 40x + 6x2) = 0 Solving 50 + 40x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(25 + 20x + 3x2) = 0 Factor a trinomial. 2((5 + x)(5 + 3x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Subproblem 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 = {-5, -1.666666667}
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