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Simplifying (2x + 1)(3x + -2) + (3x + -2)(x + -8) = 0 Reorder the terms: (1 + 2x)(3x + -2) + (3x + -2)(x + -8) = 0 Reorder the terms: (1 + 2x)(-2 + 3x) + (3x + -2)(x + -8) = 0 Multiply (1 + 2x) * (-2 + 3x) (1(-2 + 3x) + 2x * (-2 + 3x)) + (3x + -2)(x + -8) = 0 ((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) + (3x + -2)(x + -8) = 0 ((-2 + 3x) + 2x * (-2 + 3x)) + (3x + -2)(x + -8) = 0 (-2 + 3x + (-2 * 2x + 3x * 2x)) + (3x + -2)(x + -8) = 0 (-2 + 3x + (-4x + 6x2)) + (3x + -2)(x + -8) = 0 Combine like terms: 3x + -4x = -1x (-2 + -1x + 6x2) + (3x + -2)(x + -8) = 0 Reorder the terms: -2 + -1x + 6x2 + (-2 + 3x)(x + -8) = 0 Reorder the terms: -2 + -1x + 6x2 + (-2 + 3x)(-8 + x) = 0 Multiply (-2 + 3x) * (-8 + x) -2 + -1x + 6x2 + (-2(-8 + x) + 3x * (-8 + x)) = 0 -2 + -1x + 6x2 + ((-8 * -2 + x * -2) + 3x * (-8 + x)) = 0 -2 + -1x + 6x2 + ((16 + -2x) + 3x * (-8 + x)) = 0 -2 + -1x + 6x2 + (16 + -2x + (-8 * 3x + x * 3x)) = 0 -2 + -1x + 6x2 + (16 + -2x + (-24x + 3x2)) = 0 Combine like terms: -2x + -24x = -26x -2 + -1x + 6x2 + (16 + -26x + 3x2) = 0 Reorder the terms: -2 + 16 + -1x + -26x + 6x2 + 3x2 = 0 Combine like terms: -2 + 16 = 14 14 + -1x + -26x + 6x2 + 3x2 = 0 Combine like terms: -1x + -26x = -27x 14 + -27x + 6x2 + 3x2 = 0 Combine like terms: 6x2 + 3x2 = 9x2 14 + -27x + 9x2 = 0 Solving 14 + -27x + 9x2 = 0 Solving for variable 'x'. Factor a trinomial. (2 + -3x)(7 + -3x) = 0Subproblem 1
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 = 0.6666666667Subproblem 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 = {0.6666666667, 2.333333333}
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