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Simplifying 7(5x + 3)(2x + 1) = 0 Reorder the terms: 7(3 + 5x)(2x + 1) = 0 Reorder the terms: 7(3 + 5x)(1 + 2x) = 0 Multiply (3 + 5x) * (1 + 2x) 7(3(1 + 2x) + 5x * (1 + 2x)) = 0 7((1 * 3 + 2x * 3) + 5x * (1 + 2x)) = 0 7((3 + 6x) + 5x * (1 + 2x)) = 0 7(3 + 6x + (1 * 5x + 2x * 5x)) = 0 7(3 + 6x + (5x + 10x2)) = 0 Combine like terms: 6x + 5x = 11x 7(3 + 11x + 10x2) = 0 (3 * 7 + 11x * 7 + 10x2 * 7) = 0 (21 + 77x + 70x2) = 0 Solving 21 + 77x + 70x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(3 + 11x + 10x2) = 0 Factor a trinomial. 7((3 + 5x)(1 + 2x)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(3 + 5x)' equal to zero and attempt to solve: Simplifying 3 + 5x = 0 Solving 3 + 5x = 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 + 5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5x = 0 + -3 5x = 0 + -3 Combine like terms: 0 + -3 = -3 5x = -3 Divide each side by '5'. x = -0.6 Simplifying x = -0.6Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-0.6, -0.5}
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