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Simplifying (2x + 6)(x + 7) = 0 Reorder the terms: (6 + 2x)(x + 7) = 0 Reorder the terms: (6 + 2x)(7 + x) = 0 Multiply (6 + 2x) * (7 + x) (6(7 + x) + 2x * (7 + x)) = 0 ((7 * 6 + x * 6) + 2x * (7 + x)) = 0 ((42 + 6x) + 2x * (7 + x)) = 0 (42 + 6x + (7 * 2x + x * 2x)) = 0 (42 + 6x + (14x + 2x2)) = 0 Combine like terms: 6x + 14x = 20x (42 + 20x + 2x2) = 0 Solving 42 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 10x + x2) = 0 Factor a trinomial. 2((7 + x)(3 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 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 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
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 = -3Solution
x = {-7, -3}
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