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Simplifying (2x + 6)(5x + 7) = 0 Reorder the terms: (6 + 2x)(5x + 7) = 0 Reorder the terms: (6 + 2x)(7 + 5x) = 0 Multiply (6 + 2x) * (7 + 5x) (6(7 + 5x) + 2x * (7 + 5x)) = 0 ((7 * 6 + 5x * 6) + 2x * (7 + 5x)) = 0 ((42 + 30x) + 2x * (7 + 5x)) = 0 (42 + 30x + (7 * 2x + 5x * 2x)) = 0 (42 + 30x + (14x + 10x2)) = 0 Combine like terms: 30x + 14x = 44x (42 + 44x + 10x2) = 0 Solving 42 + 44x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 22x + 5x2) = 0 Factor a trinomial. 2((3 + x)(7 + 5x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 2
Set the factor '(7 + 5x)' equal to zero and attempt to solve: Simplifying 7 + 5x = 0 Solving 7 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5x = 0 + -7 5x = 0 + -7 Combine like terms: 0 + -7 = -7 5x = -7 Divide each side by '5'. x = -1.4 Simplifying x = -1.4Solution
x = {-3, -1.4}
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