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Simplifying (2x + 7)(3x + 12) = 0 Reorder the terms: (7 + 2x)(3x + 12) = 0 Reorder the terms: (7 + 2x)(12 + 3x) = 0 Multiply (7 + 2x) * (12 + 3x) (7(12 + 3x) + 2x * (12 + 3x)) = 0 ((12 * 7 + 3x * 7) + 2x * (12 + 3x)) = 0 ((84 + 21x) + 2x * (12 + 3x)) = 0 (84 + 21x + (12 * 2x + 3x * 2x)) = 0 (84 + 21x + (24x + 6x2)) = 0 Combine like terms: 21x + 24x = 45x (84 + 45x + 6x2) = 0 Solving 84 + 45x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(28 + 15x + 2x2) = 0 Factor a trinomial. 3((4 + x)(7 + 2x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Subproblem 2
Set the factor '(7 + 2x)' equal to zero and attempt to solve: Simplifying 7 + 2x = 0 Solving 7 + 2x = 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 + 2x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2x = 0 + -7 2x = 0 + -7 Combine like terms: 0 + -7 = -7 2x = -7 Divide each side by '2'. x = -3.5 Simplifying x = -3.5Solution
x = {-4, -3.5}
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