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Simplifying (3x + 9)(6x + 7) = 0 Reorder the terms: (9 + 3x)(6x + 7) = 0 Reorder the terms: (9 + 3x)(7 + 6x) = 0 Multiply (9 + 3x) * (7 + 6x) (9(7 + 6x) + 3x * (7 + 6x)) = 0 ((7 * 9 + 6x * 9) + 3x * (7 + 6x)) = 0 ((63 + 54x) + 3x * (7 + 6x)) = 0 (63 + 54x + (7 * 3x + 6x * 3x)) = 0 (63 + 54x + (21x + 18x2)) = 0 Combine like terms: 54x + 21x = 75x (63 + 75x + 18x2) = 0 Solving 63 + 75x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(21 + 25x + 6x2) = 0 Factor a trinomial. 3((3 + x)(7 + 6x)) = 0 Ignore the factor 3.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 + 6x)' equal to zero and attempt to solve: Simplifying 7 + 6x = 0 Solving 7 + 6x = 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 + 6x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6x = 0 + -7 6x = 0 + -7 Combine like terms: 0 + -7 = -7 6x = -7 Divide each side by '6'. x = -1.166666667 Simplifying x = -1.166666667Solution
x = {-3, -1.166666667}
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