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Simplifying (1 + x)(3x + 4) + -1(2x + 1)(x + -3) = x(x + -4) + 23 Reorder the terms: (1 + x)(4 + 3x) + -1(2x + 1)(x + -3) = x(x + -4) + 23 Multiply (1 + x) * (4 + 3x) (1(4 + 3x) + x(4 + 3x)) + -1(2x + 1)(x + -3) = x(x + -4) + 23 ((4 * 1 + 3x * 1) + x(4 + 3x)) + -1(2x + 1)(x + -3) = x(x + -4) + 23 ((4 + 3x) + x(4 + 3x)) + -1(2x + 1)(x + -3) = x(x + -4) + 23 (4 + 3x + (4 * x + 3x * x)) + -1(2x + 1)(x + -3) = x(x + -4) + 23 (4 + 3x + (4x + 3x2)) + -1(2x + 1)(x + -3) = x(x + -4) + 23 Combine like terms: 3x + 4x = 7x (4 + 7x + 3x2) + -1(2x + 1)(x + -3) = x(x + -4) + 23 Reorder the terms: 4 + 7x + 3x2 + -1(1 + 2x)(x + -3) = x(x + -4) + 23 Reorder the terms: 4 + 7x + 3x2 + -1(1 + 2x)(-3 + x) = x(x + -4) + 23 Multiply (1 + 2x) * (-3 + x) 4 + 7x + 3x2 + -1(1(-3 + x) + 2x * (-3 + x)) = x(x + -4) + 23 4 + 7x + 3x2 + -1((-3 * 1 + x * 1) + 2x * (-3 + x)) = x(x + -4) + 23 4 + 7x + 3x2 + -1((-3 + 1x) + 2x * (-3 + x)) = x(x + -4) + 23 4 + 7x + 3x2 + -1(-3 + 1x + (-3 * 2x + x * 2x)) = x(x + -4) + 23 4 + 7x + 3x2 + -1(-3 + 1x + (-6x + 2x2)) = x(x + -4) + 23 Combine like terms: 1x + -6x = -5x 4 + 7x + 3x2 + -1(-3 + -5x + 2x2) = x(x + -4) + 23 4 + 7x + 3x2 + (-3 * -1 + -5x * -1 + 2x2 * -1) = x(x + -4) + 23 4 + 7x + 3x2 + (3 + 5x + -2x2) = x(x + -4) + 23 Reorder the terms: 4 + 3 + 7x + 5x + 3x2 + -2x2 = x(x + -4) + 23 Combine like terms: 4 + 3 = 7 7 + 7x + 5x + 3x2 + -2x2 = x(x + -4) + 23 Combine like terms: 7x + 5x = 12x 7 + 12x + 3x2 + -2x2 = x(x + -4) + 23 Combine like terms: 3x2 + -2x2 = 1x2 7 + 12x + 1x2 = x(x + -4) + 23 Reorder the terms: 7 + 12x + 1x2 = x(-4 + x) + 23 7 + 12x + 1x2 = (-4 * x + x * x) + 23 7 + 12x + 1x2 = (-4x + x2) + 23 Reorder the terms: 7 + 12x + 1x2 = 23 + -4x + x2 Solving 7 + 12x + 1x2 = 23 + -4x + x2 Solving for variable 'x'. Reorder the terms: 7 + -23 + 12x + 4x + 1x2 + -1x2 = 23 + -4x + x2 + -23 + 4x + -1x2 Combine like terms: 7 + -23 = -16 -16 + 12x + 4x + 1x2 + -1x2 = 23 + -4x + x2 + -23 + 4x + -1x2 Combine like terms: 12x + 4x = 16x -16 + 16x + 1x2 + -1x2 = 23 + -4x + x2 + -23 + 4x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -16 + 16x + 0 = 23 + -4x + x2 + -23 + 4x + -1x2 -16 + 16x = 23 + -4x + x2 + -23 + 4x + -1x2 Reorder the terms: -16 + 16x = 23 + -23 + -4x + 4x + x2 + -1x2 Combine like terms: 23 + -23 = 0 -16 + 16x = 0 + -4x + 4x + x2 + -1x2 -16 + 16x = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -16 + 16x = 0 + x2 + -1x2 -16 + 16x = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + 16x = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-1 + x) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {1}
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