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Simplifying (x + -8)(4x + 3) + -1(x + -8)(x + -2) = 0 Reorder the terms: (-8 + x)(4x + 3) + -1(x + -8)(x + -2) = 0 Reorder the terms: (-8 + x)(3 + 4x) + -1(x + -8)(x + -2) = 0 Multiply (-8 + x) * (3 + 4x) (-8(3 + 4x) + x(3 + 4x)) + -1(x + -8)(x + -2) = 0 ((3 * -8 + 4x * -8) + x(3 + 4x)) + -1(x + -8)(x + -2) = 0 ((-24 + -32x) + x(3 + 4x)) + -1(x + -8)(x + -2) = 0 (-24 + -32x + (3 * x + 4x * x)) + -1(x + -8)(x + -2) = 0 (-24 + -32x + (3x + 4x2)) + -1(x + -8)(x + -2) = 0 Combine like terms: -32x + 3x = -29x (-24 + -29x + 4x2) + -1(x + -8)(x + -2) = 0 Reorder the terms: -24 + -29x + 4x2 + -1(-8 + x)(x + -2) = 0 Reorder the terms: -24 + -29x + 4x2 + -1(-8 + x)(-2 + x) = 0 Multiply (-8 + x) * (-2 + x) -24 + -29x + 4x2 + -1(-8(-2 + x) + x(-2 + x)) = 0 -24 + -29x + 4x2 + -1((-2 * -8 + x * -8) + x(-2 + x)) = 0 -24 + -29x + 4x2 + -1((16 + -8x) + x(-2 + x)) = 0 -24 + -29x + 4x2 + -1(16 + -8x + (-2 * x + x * x)) = 0 -24 + -29x + 4x2 + -1(16 + -8x + (-2x + x2)) = 0 Combine like terms: -8x + -2x = -10x -24 + -29x + 4x2 + -1(16 + -10x + x2) = 0 -24 + -29x + 4x2 + (16 * -1 + -10x * -1 + x2 * -1) = 0 -24 + -29x + 4x2 + (-16 + 10x + -1x2) = 0 Reorder the terms: -24 + -16 + -29x + 10x + 4x2 + -1x2 = 0 Combine like terms: -24 + -16 = -40 -40 + -29x + 10x + 4x2 + -1x2 = 0 Combine like terms: -29x + 10x = -19x -40 + -19x + 4x2 + -1x2 = 0 Combine like terms: 4x2 + -1x2 = 3x2 -40 + -19x + 3x2 = 0 Solving -40 + -19x + 3x2 = 0 Solving for variable 'x'. Factor a trinomial. (-5 + -3x)(8 + -1x) = 0Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve: Simplifying -5 + -3x = 0 Solving -5 + -3x = 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 + -3x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3x = 0 + 5 -3x = 0 + 5 Combine like terms: 0 + 5 = 5 -3x = 5 Divide each side by '-3'. x = -1.666666667 Simplifying x = -1.666666667Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-1.666666667, 8}
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