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Simplifying (3x + 2)(6x + 7) = 0 Reorder the terms: (2 + 3x)(6x + 7) = 0 Reorder the terms: (2 + 3x)(7 + 6x) = 0 Multiply (2 + 3x) * (7 + 6x) (2(7 + 6x) + 3x * (7 + 6x)) = 0 ((7 * 2 + 6x * 2) + 3x * (7 + 6x)) = 0 ((14 + 12x) + 3x * (7 + 6x)) = 0 (14 + 12x + (7 * 3x + 6x * 3x)) = 0 (14 + 12x + (21x + 18x2)) = 0 Combine like terms: 12x + 21x = 33x (14 + 33x + 18x2) = 0 Solving 14 + 33x + 18x2 = 0 Solving for variable 'x'. Factor a trinomial. (7 + 6x)(2 + 3x) = 0Subproblem 1
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 = -1.166666667Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667Solution
x = {-1.166666667, -0.6666666667}
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