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Simplifying 7(3x + 2) * 2(1 + -1x) + (3x + 2)(1 + -1x) * 3 = 0 Reorder the terms: 7(2 + 3x) * 2(1 + -1x) + (3x + 2)(1 + -1x) * 3 = 0 Reorder the terms for easier multiplication: 7 * 2(2 + 3x)(1 + -1x) + (3x + 2)(1 + -1x) * 3 = 0 Multiply 7 * 2 14(2 + 3x)(1 + -1x) + (3x + 2)(1 + -1x) * 3 = 0 Multiply (2 + 3x) * (1 + -1x) 14(2(1 + -1x) + 3x * (1 + -1x)) + (3x + 2)(1 + -1x) * 3 = 0 14((1 * 2 + -1x * 2) + 3x * (1 + -1x)) + (3x + 2)(1 + -1x) * 3 = 0 14((2 + -2x) + 3x * (1 + -1x)) + (3x + 2)(1 + -1x) * 3 = 0 14(2 + -2x + (1 * 3x + -1x * 3x)) + (3x + 2)(1 + -1x) * 3 = 0 14(2 + -2x + (3x + -3x2)) + (3x + 2)(1 + -1x) * 3 = 0 Combine like terms: -2x + 3x = 1x 14(2 + 1x + -3x2) + (3x + 2)(1 + -1x) * 3 = 0 (2 * 14 + 1x * 14 + -3x2 * 14) + (3x + 2)(1 + -1x) * 3 = 0 (28 + 14x + -42x2) + (3x + 2)(1 + -1x) * 3 = 0 Reorder the terms: 28 + 14x + -42x2 + (2 + 3x)(1 + -1x) * 3 = 0 Reorder the terms for easier multiplication: 28 + 14x + -42x2 + 3(2 + 3x)(1 + -1x) = 0 Multiply (2 + 3x) * (1 + -1x) 28 + 14x + -42x2 + 3(2(1 + -1x) + 3x * (1 + -1x)) = 0 28 + 14x + -42x2 + 3((1 * 2 + -1x * 2) + 3x * (1 + -1x)) = 0 28 + 14x + -42x2 + 3((2 + -2x) + 3x * (1 + -1x)) = 0 28 + 14x + -42x2 + 3(2 + -2x + (1 * 3x + -1x * 3x)) = 0 28 + 14x + -42x2 + 3(2 + -2x + (3x + -3x2)) = 0 Combine like terms: -2x + 3x = 1x 28 + 14x + -42x2 + 3(2 + 1x + -3x2) = 0 28 + 14x + -42x2 + (2 * 3 + 1x * 3 + -3x2 * 3) = 0 28 + 14x + -42x2 + (6 + 3x + -9x2) = 0 Reorder the terms: 28 + 6 + 14x + 3x + -42x2 + -9x2 = 0 Combine like terms: 28 + 6 = 34 34 + 14x + 3x + -42x2 + -9x2 = 0 Combine like terms: 14x + 3x = 17x 34 + 17x + -42x2 + -9x2 = 0 Combine like terms: -42x2 + -9x2 = -51x2 34 + 17x + -51x2 = 0 Solving 34 + 17x + -51x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '17'. 17(2 + x + -3x2) = 0 Factor a trinomial. 17((1 + -1x)(2 + 3x)) = 0 Ignore the factor 17.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 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, -0.6666666667}
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