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Simplifying (3x + 3)(7x + 5) = 0 Reorder the terms: (3 + 3x)(7x + 5) = 0 Reorder the terms: (3 + 3x)(5 + 7x) = 0 Multiply (3 + 3x) * (5 + 7x) (3(5 + 7x) + 3x * (5 + 7x)) = 0 ((5 * 3 + 7x * 3) + 3x * (5 + 7x)) = 0 ((15 + 21x) + 3x * (5 + 7x)) = 0 (15 + 21x + (5 * 3x + 7x * 3x)) = 0 (15 + 21x + (15x + 21x2)) = 0 Combine like terms: 21x + 15x = 36x (15 + 36x + 21x2) = 0 Solving 15 + 36x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + 12x + 7x2) = 0 Factor a trinomial. 3((1 + x)(5 + 7x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1Subproblem 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, -0.7142857143}
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