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Simplifying (2x + 3)(9x + 6) = 43 + 2(3x + 1)(3 + 1) Reorder the terms: (3 + 2x)(9x + 6) = 43 + 2(3x + 1)(3 + 1) Reorder the terms: (3 + 2x)(6 + 9x) = 43 + 2(3x + 1)(3 + 1) Multiply (3 + 2x) * (6 + 9x) (3(6 + 9x) + 2x * (6 + 9x)) = 43 + 2(3x + 1)(3 + 1) ((6 * 3 + 9x * 3) + 2x * (6 + 9x)) = 43 + 2(3x + 1)(3 + 1) ((18 + 27x) + 2x * (6 + 9x)) = 43 + 2(3x + 1)(3 + 1) (18 + 27x + (6 * 2x + 9x * 2x)) = 43 + 2(3x + 1)(3 + 1) (18 + 27x + (12x + 18x2)) = 43 + 2(3x + 1)(3 + 1) Combine like terms: 27x + 12x = 39x (18 + 39x + 18x2) = 43 + 2(3x + 1)(3 + 1) Reorder the terms: 18 + 39x + 18x2 = 43 + 2(1 + 3x)(3 + 1) Combine like terms: 3 + 1 = 4 18 + 39x + 18x2 = 43 + 2(1 + 3x)(4) Reorder the terms for easier multiplication: 18 + 39x + 18x2 = 43 + 2 * 4(1 + 3x) Multiply 2 * 4 18 + 39x + 18x2 = 43 + 8(1 + 3x) 18 + 39x + 18x2 = 43 + (1 * 8 + 3x * 8) 18 + 39x + 18x2 = 43 + (8 + 24x) Combine like terms: 43 + 8 = 51 18 + 39x + 18x2 = 51 + 24x Solving 18 + 39x + 18x2 = 51 + 24x Solving for variable 'x'. Reorder the terms: 18 + -51 + 39x + -24x + 18x2 = 51 + 24x + -51 + -24x Combine like terms: 18 + -51 = -33 -33 + 39x + -24x + 18x2 = 51 + 24x + -51 + -24x Combine like terms: 39x + -24x = 15x -33 + 15x + 18x2 = 51 + 24x + -51 + -24x Reorder the terms: -33 + 15x + 18x2 = 51 + -51 + 24x + -24x Combine like terms: 51 + -51 = 0 -33 + 15x + 18x2 = 0 + 24x + -24x -33 + 15x + 18x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -33 + 15x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-11 + 5x + 6x2) = 0 Factor a trinomial. 3((-11 + -6x)(1 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -6x)' equal to zero and attempt to solve: Simplifying -11 + -6x = 0 Solving -11 + -6x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -6x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6x = 0 + 11 -6x = 0 + 11 Combine like terms: 0 + 11 = 11 -6x = 11 Divide each side by '-6'. x = -1.833333333 Simplifying x = -1.833333333Subproblem 2
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 = 1Solution
x = {-1.833333333, 1}
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