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Simplifying (3x + 7)(x + 6) = 0 Reorder the terms: (7 + 3x)(x + 6) = 0 Reorder the terms: (7 + 3x)(6 + x) = 0 Multiply (7 + 3x) * (6 + x) (7(6 + x) + 3x * (6 + x)) = 0 ((6 * 7 + x * 7) + 3x * (6 + x)) = 0 ((42 + 7x) + 3x * (6 + x)) = 0 (42 + 7x + (6 * 3x + x * 3x)) = 0 (42 + 7x + (18x + 3x2)) = 0 Combine like terms: 7x + 18x = 25x (42 + 25x + 3x2) = 0 Solving 42 + 25x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (6 + x)(7 + 3x) = 0Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve: Simplifying 7 + 3x = 0 Solving 7 + 3x = 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 + 3x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3x = 0 + -7 3x = 0 + -7 Combine like terms: 0 + -7 = -7 3x = -7 Divide each side by '3'. x = -2.333333333 Simplifying x = -2.333333333Solution
x = {-6, -2.333333333}
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