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Simplifying (x + 6)(2x + -1) = (2x + -1)(-6x + 13) Reorder the terms: (6 + x)(2x + -1) = (2x + -1)(-6x + 13) Reorder the terms: (6 + x)(-1 + 2x) = (2x + -1)(-6x + 13) Multiply (6 + x) * (-1 + 2x) (6(-1 + 2x) + x(-1 + 2x)) = (2x + -1)(-6x + 13) ((-1 * 6 + 2x * 6) + x(-1 + 2x)) = (2x + -1)(-6x + 13) ((-6 + 12x) + x(-1 + 2x)) = (2x + -1)(-6x + 13) (-6 + 12x + (-1 * x + 2x * x)) = (2x + -1)(-6x + 13) (-6 + 12x + (-1x + 2x2)) = (2x + -1)(-6x + 13) Combine like terms: 12x + -1x = 11x (-6 + 11x + 2x2) = (2x + -1)(-6x + 13) Reorder the terms: -6 + 11x + 2x2 = (-1 + 2x)(-6x + 13) Reorder the terms: -6 + 11x + 2x2 = (-1 + 2x)(13 + -6x) Multiply (-1 + 2x) * (13 + -6x) -6 + 11x + 2x2 = (-1(13 + -6x) + 2x * (13 + -6x)) -6 + 11x + 2x2 = ((13 * -1 + -6x * -1) + 2x * (13 + -6x)) -6 + 11x + 2x2 = ((-13 + 6x) + 2x * (13 + -6x)) -6 + 11x + 2x2 = (-13 + 6x + (13 * 2x + -6x * 2x)) -6 + 11x + 2x2 = (-13 + 6x + (26x + -12x2)) Combine like terms: 6x + 26x = 32x -6 + 11x + 2x2 = (-13 + 32x + -12x2) Solving -6 + 11x + 2x2 = -13 + 32x + -12x2 Solving for variable 'x'. Reorder the terms: -6 + 13 + 11x + -32x + 2x2 + 12x2 = -13 + 32x + -12x2 + 13 + -32x + 12x2 Combine like terms: -6 + 13 = 7 7 + 11x + -32x + 2x2 + 12x2 = -13 + 32x + -12x2 + 13 + -32x + 12x2 Combine like terms: 11x + -32x = -21x 7 + -21x + 2x2 + 12x2 = -13 + 32x + -12x2 + 13 + -32x + 12x2 Combine like terms: 2x2 + 12x2 = 14x2 7 + -21x + 14x2 = -13 + 32x + -12x2 + 13 + -32x + 12x2 Reorder the terms: 7 + -21x + 14x2 = -13 + 13 + 32x + -32x + -12x2 + 12x2 Combine like terms: -13 + 13 = 0 7 + -21x + 14x2 = 0 + 32x + -32x + -12x2 + 12x2 7 + -21x + 14x2 = 32x + -32x + -12x2 + 12x2 Combine like terms: 32x + -32x = 0 7 + -21x + 14x2 = 0 + -12x2 + 12x2 7 + -21x + 14x2 = -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 7 + -21x + 14x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(1 + -3x + 2x2) = 0 Factor a trinomial. 7((1 + -2x)(1 + -1x)) = 0 Ignore the factor 7.Subproblem 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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {0.5, 1}
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