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Simplifying (9x + 3)(5x + 10) = 0 Reorder the terms: (3 + 9x)(5x + 10) = 0 Reorder the terms: (3 + 9x)(10 + 5x) = 0 Multiply (3 + 9x) * (10 + 5x) (3(10 + 5x) + 9x * (10 + 5x)) = 0 ((10 * 3 + 5x * 3) + 9x * (10 + 5x)) = 0 ((30 + 15x) + 9x * (10 + 5x)) = 0 (30 + 15x + (10 * 9x + 5x * 9x)) = 0 (30 + 15x + (90x + 45x2)) = 0 Combine like terms: 15x + 90x = 105x (30 + 105x + 45x2) = 0 Solving 30 + 105x + 45x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(2 + 7x + 3x2) = 0 Factor a trinomial. 15((2 + x)(1 + 3x)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + 3x)' equal to zero and attempt to solve: Simplifying 1 + 3x = 0 Solving 1 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3x = 0 + -1 3x = 0 + -1 Combine like terms: 0 + -1 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333Solution
x = {-2, -0.3333333333}
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