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Simplifying (3x + 6)(x + 7) = 0 Reorder the terms: (6 + 3x)(x + 7) = 0 Reorder the terms: (6 + 3x)(7 + x) = 0 Multiply (6 + 3x) * (7 + x) (6(7 + x) + 3x * (7 + x)) = 0 ((7 * 6 + x * 6) + 3x * (7 + x)) = 0 ((42 + 6x) + 3x * (7 + x)) = 0 (42 + 6x + (7 * 3x + x * 3x)) = 0 (42 + 6x + (21x + 3x2)) = 0 Combine like terms: 6x + 21x = 27x (42 + 27x + 3x2) = 0 Solving 42 + 27x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 9x + x2) = 0 Factor a trinomial. 3((7 + x)(2 + x)) = 0 Ignore the factor 3.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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-7, -2}
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