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Simplifying (5x + 3)(7x + 7) = 0 Reorder the terms: (3 + 5x)(7x + 7) = 0 Reorder the terms: (3 + 5x)(7 + 7x) = 0 Multiply (3 + 5x) * (7 + 7x) (3(7 + 7x) + 5x * (7 + 7x)) = 0 ((7 * 3 + 7x * 3) + 5x * (7 + 7x)) = 0 ((21 + 21x) + 5x * (7 + 7x)) = 0 (21 + 21x + (7 * 5x + 7x * 5x)) = 0 (21 + 21x + (35x + 35x2)) = 0 Combine like terms: 21x + 35x = 56x (21 + 56x + 35x2) = 0 Solving 21 + 56x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '7'. 7(3 + 8x + 5x2) = 0 Factor a trinomial. 7((1 + x)(3 + 5x)) = 0 Ignore the factor 7.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 '(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 = -0.6Solution
x = {-1, -0.6}
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