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Simplifying (x + 4)(x + 1) = x + -1(x + -2)(2 + -1x) Reorder the terms: (4 + x)(x + 1) = x + -1(x + -2)(2 + -1x) Reorder the terms: (4 + x)(1 + x) = x + -1(x + -2)(2 + -1x) Multiply (4 + x) * (1 + x) (4(1 + x) + x(1 + x)) = x + -1(x + -2)(2 + -1x) ((1 * 4 + x * 4) + x(1 + x)) = x + -1(x + -2)(2 + -1x) ((4 + 4x) + x(1 + x)) = x + -1(x + -2)(2 + -1x) (4 + 4x + (1 * x + x * x)) = x + -1(x + -2)(2 + -1x) (4 + 4x + (1x + x2)) = x + -1(x + -2)(2 + -1x) Combine like terms: 4x + 1x = 5x (4 + 5x + x2) = x + -1(x + -2)(2 + -1x) Reorder the terms: 4 + 5x + x2 = x + -1(-2 + x)(2 + -1x) Multiply (-2 + x) * (2 + -1x) 4 + 5x + x2 = x + -1(-2(2 + -1x) + x(2 + -1x)) 4 + 5x + x2 = x + -1((2 * -2 + -1x * -2) + x(2 + -1x)) 4 + 5x + x2 = x + -1((-4 + 2x) + x(2 + -1x)) 4 + 5x + x2 = x + -1(-4 + 2x + (2 * x + -1x * x)) 4 + 5x + x2 = x + -1(-4 + 2x + (2x + -1x2)) Combine like terms: 2x + 2x = 4x 4 + 5x + x2 = x + -1(-4 + 4x + -1x2) 4 + 5x + x2 = x + (-4 * -1 + 4x * -1 + -1x2 * -1) 4 + 5x + x2 = x + (4 + -4x + 1x2) Reorder the terms: 4 + 5x + x2 = 4 + x + -4x + 1x2 Combine like terms: x + -4x = -3x 4 + 5x + x2 = 4 + -3x + 1x2 Add '-4' to each side of the equation. 4 + 5x + -4 + x2 = 4 + -3x + -4 + 1x2 Reorder the terms: 4 + -4 + 5x + x2 = 4 + -3x + -4 + 1x2 Combine like terms: 4 + -4 = 0 0 + 5x + x2 = 4 + -3x + -4 + 1x2 5x + x2 = 4 + -3x + -4 + 1x2 Reorder the terms: 5x + x2 = 4 + -4 + -3x + 1x2 Combine like terms: 4 + -4 = 0 5x + x2 = 0 + -3x + 1x2 5x + x2 = -3x + 1x2 Solving 5x + x2 = -3x + 1x2 Solving for variable 'x'. Reorder the terms: 5x + 3x + x2 + -1x2 = -3x + 1x2 + 3x + -1x2 Combine like terms: 5x + 3x = 8x 8x + x2 + -1x2 = -3x + 1x2 + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 8x + 0 = -3x + 1x2 + 3x + -1x2 8x = -3x + 1x2 + 3x + -1x2 Reorder the terms: 8x = -3x + 3x + 1x2 + -1x2 Combine like terms: -3x + 3x = 0 8x = 0 + 1x2 + -1x2 8x = 1x2 + -1x2 Combine like terms: 1x2 + -1x2 = 0 8x = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Solution
x = {0}
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