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Simplifying (x + 1)[2(3x + -1) + -1(4 + 5x)] = 2(x + -1)(x + 2) + 4 Reorder the terms: (1 + x)[2(3x + -1) + -1(4 + 5x)] = 2(x + -1)(x + 2) + 4 Reorder the terms: (1 + x)[2(-1 + 3x) + -1(4 + 5x)] = 2(x + -1)(x + 2) + 4 (1 + x)[(-1 * 2 + 3x * 2) + -1(4 + 5x)] = 2(x + -1)(x + 2) + 4 (1 + x)[(-2 + 6x) + -1(4 + 5x)] = 2(x + -1)(x + 2) + 4 (1 + x)[-2 + 6x + (4 * -1 + 5x * -1)] = 2(x + -1)(x + 2) + 4 (1 + x)[-2 + 6x + (-4 + -5x)] = 2(x + -1)(x + 2) + 4 Reorder the terms: (1 + x)[-2 + -4 + 6x + -5x] = 2(x + -1)(x + 2) + 4 Combine like terms: -2 + -4 = -6 (1 + x)[-6 + 6x + -5x] = 2(x + -1)(x + 2) + 4 Combine like terms: 6x + -5x = 1x (1 + x)[-6 + 1x] = 2(x + -1)(x + 2) + 4 Multiply (1 + x) * [-6 + 1x] (1[-6 + 1x] + x[-6 + 1x]) = 2(x + -1)(x + 2) + 4 ([-6 * 1 + 1x * 1] + x[-6 + 1x]) = 2(x + -1)(x + 2) + 4 ([-6 + 1x] + x[-6 + 1x]) = 2(x + -1)(x + 2) + 4 (-6 + 1x + [-6 * x + 1x * x]) = 2(x + -1)(x + 2) + 4 (-6 + 1x + [-6x + 1x2]) = 2(x + -1)(x + 2) + 4 Combine like terms: 1x + -6x = -5x (-6 + -5x + 1x2) = 2(x + -1)(x + 2) + 4 Reorder the terms: -6 + -5x + 1x2 = 2(-1 + x)(x + 2) + 4 Reorder the terms: -6 + -5x + 1x2 = 2(-1 + x)(2 + x) + 4 Multiply (-1 + x) * (2 + x) -6 + -5x + 1x2 = 2(-1(2 + x) + x(2 + x)) + 4 -6 + -5x + 1x2 = 2((2 * -1 + x * -1) + x(2 + x)) + 4 -6 + -5x + 1x2 = 2((-2 + -1x) + x(2 + x)) + 4 -6 + -5x + 1x2 = 2(-2 + -1x + (2 * x + x * x)) + 4 -6 + -5x + 1x2 = 2(-2 + -1x + (2x + x2)) + 4 Combine like terms: -1x + 2x = 1x -6 + -5x + 1x2 = 2(-2 + 1x + x2) + 4 -6 + -5x + 1x2 = (-2 * 2 + 1x * 2 + x2 * 2) + 4 -6 + -5x + 1x2 = (-4 + 2x + 2x2) + 4 Reorder the terms: -6 + -5x + 1x2 = -4 + 4 + 2x + 2x2 Combine like terms: -4 + 4 = 0 -6 + -5x + 1x2 = 0 + 2x + 2x2 -6 + -5x + 1x2 = 2x + 2x2 Solving -6 + -5x + 1x2 = 2x + 2x2 Solving for variable 'x'. Reorder the terms: -6 + -5x + -2x + 1x2 + -2x2 = 2x + 2x2 + -2x + -2x2 Combine like terms: -5x + -2x = -7x -6 + -7x + 1x2 + -2x2 = 2x + 2x2 + -2x + -2x2 Combine like terms: 1x2 + -2x2 = -1x2 -6 + -7x + -1x2 = 2x + 2x2 + -2x + -2x2 Reorder the terms: -6 + -7x + -1x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 -6 + -7x + -1x2 = 0 + 2x2 + -2x2 -6 + -7x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -7x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 7x + x2) = 0 Factor a trinomial. -1((6 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 2
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 = {-6, -1}
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