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Simplifying 3(2x + 3)(7x + 5) = 0 Reorder the terms: 3(3 + 2x)(7x + 5) = 0 Reorder the terms: 3(3 + 2x)(5 + 7x) = 0 Multiply (3 + 2x) * (5 + 7x) 3(3(5 + 7x) + 2x * (5 + 7x)) = 0 3((5 * 3 + 7x * 3) + 2x * (5 + 7x)) = 0 3((15 + 21x) + 2x * (5 + 7x)) = 0 3(15 + 21x + (5 * 2x + 7x * 2x)) = 0 3(15 + 21x + (10x + 14x2)) = 0 Combine like terms: 21x + 10x = 31x 3(15 + 31x + 14x2) = 0 (15 * 3 + 31x * 3 + 14x2 * 3) = 0 (45 + 93x + 42x2) = 0 Solving 45 + 93x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 31x + 14x2) = 0 Factor a trinomial. 3((3 + 2x)(5 + 7x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 2
Set the factor '(5 + 7x)' equal to zero and attempt to solve: Simplifying 5 + 7x = 0 Solving 5 + 7x = 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 + 7x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 7x = 0 + -5 7x = 0 + -5 Combine like terms: 0 + -5 = -5 7x = -5 Divide each side by '7'. x = -0.7142857143 Simplifying x = -0.7142857143Solution
x = {-1.5, -0.7142857143}
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