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Simplifying (3x + -2)(3x + -2)(3) = (3x + -2)(5) + 2 Reorder the terms: (-2 + 3x)(3x + -2)(3) = (3x + -2)(5) + 2 Reorder the terms: (-2 + 3x)(-2 + 3x)(3) = (3x + -2)(5) + 2 Reorder the terms for easier multiplication: 3(-2 + 3x)(-2 + 3x) = (3x + -2)(5) + 2 Multiply (-2 + 3x) * (-2 + 3x) 3(-2(-2 + 3x) + 3x * (-2 + 3x)) = (3x + -2)(5) + 2 3((-2 * -2 + 3x * -2) + 3x * (-2 + 3x)) = (3x + -2)(5) + 2 3((4 + -6x) + 3x * (-2 + 3x)) = (3x + -2)(5) + 2 3(4 + -6x + (-2 * 3x + 3x * 3x)) = (3x + -2)(5) + 2 3(4 + -6x + (-6x + 9x2)) = (3x + -2)(5) + 2 Combine like terms: -6x + -6x = -12x 3(4 + -12x + 9x2) = (3x + -2)(5) + 2 (4 * 3 + -12x * 3 + 9x2 * 3) = (3x + -2)(5) + 2 (12 + -36x + 27x2) = (3x + -2)(5) + 2 Reorder the terms: 12 + -36x + 27x2 = (-2 + 3x)(5) + 2 Reorder the terms for easier multiplication: 12 + -36x + 27x2 = 5(-2 + 3x) + 2 12 + -36x + 27x2 = (-2 * 5 + 3x * 5) + 2 12 + -36x + 27x2 = (-10 + 15x) + 2 Reorder the terms: 12 + -36x + 27x2 = -10 + 2 + 15x Combine like terms: -10 + 2 = -8 12 + -36x + 27x2 = -8 + 15x Solving 12 + -36x + 27x2 = -8 + 15x Solving for variable 'x'. Reorder the terms: 12 + 8 + -36x + -15x + 27x2 = -8 + 15x + 8 + -15x Combine like terms: 12 + 8 = 20 20 + -36x + -15x + 27x2 = -8 + 15x + 8 + -15x Combine like terms: -36x + -15x = -51x 20 + -51x + 27x2 = -8 + 15x + 8 + -15x Reorder the terms: 20 + -51x + 27x2 = -8 + 8 + 15x + -15x Combine like terms: -8 + 8 = 0 20 + -51x + 27x2 = 0 + 15x + -15x 20 + -51x + 27x2 = 15x + -15x Combine like terms: 15x + -15x = 0 20 + -51x + 27x2 = 0 Factor a trinomial. (5 + -9x)(4 + -3x) = 0Subproblem 1
Set the factor '(5 + -9x)' equal to zero and attempt to solve: Simplifying 5 + -9x = 0 Solving 5 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -9x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9x = 0 + -5 -9x = 0 + -5 Combine like terms: 0 + -5 = -5 -9x = -5 Divide each side by '-9'. x = 0.5555555556 Simplifying x = 0.5555555556Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve: Simplifying 4 + -3x = 0 Solving 4 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3x = 0 + -4 -3x = 0 + -4 Combine like terms: 0 + -4 = -4 -3x = -4 Divide each side by '-3'. x = 1.333333333 Simplifying x = 1.333333333Solution
x = {0.5555555556, 1.333333333}
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