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Simplifying (2x + -1)(3x + -2) + 7(4 + -8x)(x + 5) = 0 Reorder the terms: (-1 + 2x)(3x + -2) + 7(4 + -8x)(x + 5) = 0 Reorder the terms: (-1 + 2x)(-2 + 3x) + 7(4 + -8x)(x + 5) = 0 Multiply (-1 + 2x) * (-2 + 3x) (-1(-2 + 3x) + 2x * (-2 + 3x)) + 7(4 + -8x)(x + 5) = 0 ((-2 * -1 + 3x * -1) + 2x * (-2 + 3x)) + 7(4 + -8x)(x + 5) = 0 ((2 + -3x) + 2x * (-2 + 3x)) + 7(4 + -8x)(x + 5) = 0 (2 + -3x + (-2 * 2x + 3x * 2x)) + 7(4 + -8x)(x + 5) = 0 (2 + -3x + (-4x + 6x2)) + 7(4 + -8x)(x + 5) = 0 Combine like terms: -3x + -4x = -7x (2 + -7x + 6x2) + 7(4 + -8x)(x + 5) = 0 Reorder the terms: 2 + -7x + 6x2 + 7(4 + -8x)(5 + x) = 0 Multiply (4 + -8x) * (5 + x) 2 + -7x + 6x2 + 7(4(5 + x) + -8x * (5 + x)) = 0 2 + -7x + 6x2 + 7((5 * 4 + x * 4) + -8x * (5 + x)) = 0 2 + -7x + 6x2 + 7((20 + 4x) + -8x * (5 + x)) = 0 2 + -7x + 6x2 + 7(20 + 4x + (5 * -8x + x * -8x)) = 0 2 + -7x + 6x2 + 7(20 + 4x + (-40x + -8x2)) = 0 Combine like terms: 4x + -40x = -36x 2 + -7x + 6x2 + 7(20 + -36x + -8x2) = 0 2 + -7x + 6x2 + (20 * 7 + -36x * 7 + -8x2 * 7) = 0 2 + -7x + 6x2 + (140 + -252x + -56x2) = 0 Reorder the terms: 2 + 140 + -7x + -252x + 6x2 + -56x2 = 0 Combine like terms: 2 + 140 = 142 142 + -7x + -252x + 6x2 + -56x2 = 0 Combine like terms: -7x + -252x = -259x 142 + -259x + 6x2 + -56x2 = 0 Combine like terms: 6x2 + -56x2 = -50x2 142 + -259x + -50x2 = 0 Solving 142 + -259x + -50x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -2x)(142 + 25x) = 0Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 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 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(142 + 25x)' equal to zero and attempt to solve: Simplifying 142 + 25x = 0 Solving 142 + 25x = 0 Move all terms containing x to the left, all other terms to the right. Add '-142' to each side of the equation. 142 + -142 + 25x = 0 + -142 Combine like terms: 142 + -142 = 0 0 + 25x = 0 + -142 25x = 0 + -142 Combine like terms: 0 + -142 = -142 25x = -142 Divide each side by '25'. x = -5.68 Simplifying x = -5.68Solution
x = {0.5, -5.68}
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