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Simplifying (2x + -1)(x + 5) + -1(2x + -1)(4x + 3) = 0 Reorder the terms: (-1 + 2x)(x + 5) + -1(2x + -1)(4x + 3) = 0 Reorder the terms: (-1 + 2x)(5 + x) + -1(2x + -1)(4x + 3) = 0 Multiply (-1 + 2x) * (5 + x) (-1(5 + x) + 2x * (5 + x)) + -1(2x + -1)(4x + 3) = 0 ((5 * -1 + x * -1) + 2x * (5 + x)) + -1(2x + -1)(4x + 3) = 0 ((-5 + -1x) + 2x * (5 + x)) + -1(2x + -1)(4x + 3) = 0 (-5 + -1x + (5 * 2x + x * 2x)) + -1(2x + -1)(4x + 3) = 0 (-5 + -1x + (10x + 2x2)) + -1(2x + -1)(4x + 3) = 0 Combine like terms: -1x + 10x = 9x (-5 + 9x + 2x2) + -1(2x + -1)(4x + 3) = 0 Reorder the terms: -5 + 9x + 2x2 + -1(-1 + 2x)(4x + 3) = 0 Reorder the terms: -5 + 9x + 2x2 + -1(-1 + 2x)(3 + 4x) = 0 Multiply (-1 + 2x) * (3 + 4x) -5 + 9x + 2x2 + -1(-1(3 + 4x) + 2x * (3 + 4x)) = 0 -5 + 9x + 2x2 + -1((3 * -1 + 4x * -1) + 2x * (3 + 4x)) = 0 -5 + 9x + 2x2 + -1((-3 + -4x) + 2x * (3 + 4x)) = 0 -5 + 9x + 2x2 + -1(-3 + -4x + (3 * 2x + 4x * 2x)) = 0 -5 + 9x + 2x2 + -1(-3 + -4x + (6x + 8x2)) = 0 Combine like terms: -4x + 6x = 2x -5 + 9x + 2x2 + -1(-3 + 2x + 8x2) = 0 -5 + 9x + 2x2 + (-3 * -1 + 2x * -1 + 8x2 * -1) = 0 -5 + 9x + 2x2 + (3 + -2x + -8x2) = 0 Reorder the terms: -5 + 3 + 9x + -2x + 2x2 + -8x2 = 0 Combine like terms: -5 + 3 = -2 -2 + 9x + -2x + 2x2 + -8x2 = 0 Combine like terms: 9x + -2x = 7x -2 + 7x + 2x2 + -8x2 = 0 Combine like terms: 2x2 + -8x2 = -6x2 -2 + 7x + -6x2 = 0 Solving -2 + 7x + -6x2 = 0 Solving for variable 'x'. Factor a trinomial. (-2 + 3x)(1 + -2x) = 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 '(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 = 0.5Solution
x = {0.6666666667, 0.5}
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