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Simplifying (2x + -1)(-1x + 5) = (4x + 3)(2x + -1) Reorder the terms: (-1 + 2x)(-1x + 5) = (4x + 3)(2x + -1) Reorder the terms: (-1 + 2x)(5 + -1x) = (4x + 3)(2x + -1) Multiply (-1 + 2x) * (5 + -1x) (-1(5 + -1x) + 2x * (5 + -1x)) = (4x + 3)(2x + -1) ((5 * -1 + -1x * -1) + 2x * (5 + -1x)) = (4x + 3)(2x + -1) ((-5 + 1x) + 2x * (5 + -1x)) = (4x + 3)(2x + -1) (-5 + 1x + (5 * 2x + -1x * 2x)) = (4x + 3)(2x + -1) (-5 + 1x + (10x + -2x2)) = (4x + 3)(2x + -1) Combine like terms: 1x + 10x = 11x (-5 + 11x + -2x2) = (4x + 3)(2x + -1) Reorder the terms: -5 + 11x + -2x2 = (3 + 4x)(2x + -1) Reorder the terms: -5 + 11x + -2x2 = (3 + 4x)(-1 + 2x) Multiply (3 + 4x) * (-1 + 2x) -5 + 11x + -2x2 = (3(-1 + 2x) + 4x * (-1 + 2x)) -5 + 11x + -2x2 = ((-1 * 3 + 2x * 3) + 4x * (-1 + 2x)) -5 + 11x + -2x2 = ((-3 + 6x) + 4x * (-1 + 2x)) -5 + 11x + -2x2 = (-3 + 6x + (-1 * 4x + 2x * 4x)) -5 + 11x + -2x2 = (-3 + 6x + (-4x + 8x2)) Combine like terms: 6x + -4x = 2x -5 + 11x + -2x2 = (-3 + 2x + 8x2) Solving -5 + 11x + -2x2 = -3 + 2x + 8x2 Solving for variable 'x'. Reorder the terms: -5 + 3 + 11x + -2x + -2x2 + -8x2 = -3 + 2x + 8x2 + 3 + -2x + -8x2 Combine like terms: -5 + 3 = -2 -2 + 11x + -2x + -2x2 + -8x2 = -3 + 2x + 8x2 + 3 + -2x + -8x2 Combine like terms: 11x + -2x = 9x -2 + 9x + -2x2 + -8x2 = -3 + 2x + 8x2 + 3 + -2x + -8x2 Combine like terms: -2x2 + -8x2 = -10x2 -2 + 9x + -10x2 = -3 + 2x + 8x2 + 3 + -2x + -8x2 Reorder the terms: -2 + 9x + -10x2 = -3 + 3 + 2x + -2x + 8x2 + -8x2 Combine like terms: -3 + 3 = 0 -2 + 9x + -10x2 = 0 + 2x + -2x + 8x2 + -8x2 -2 + 9x + -10x2 = 2x + -2x + 8x2 + -8x2 Combine like terms: 2x + -2x = 0 -2 + 9x + -10x2 = 0 + 8x2 + -8x2 -2 + 9x + -10x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -2 + 9x + -10x2 = 0 Factor a trinomial. (-1 + 2x)(2 + -5x) = 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 '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 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 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {0.5, 0.4}
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