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Simplifying (x + 2)(x + 4) = 4(x + 2x + 4) + -1 Reorder the terms: (2 + x)(x + 4) = 4(x + 2x + 4) + -1 Reorder the terms: (2 + x)(4 + x) = 4(x + 2x + 4) + -1 Multiply (2 + x) * (4 + x) (2(4 + x) + x(4 + x)) = 4(x + 2x + 4) + -1 ((4 * 2 + x * 2) + x(4 + x)) = 4(x + 2x + 4) + -1 ((8 + 2x) + x(4 + x)) = 4(x + 2x + 4) + -1 (8 + 2x + (4 * x + x * x)) = 4(x + 2x + 4) + -1 (8 + 2x + (4x + x2)) = 4(x + 2x + 4) + -1 Combine like terms: 2x + 4x = 6x (8 + 6x + x2) = 4(x + 2x + 4) + -1 Reorder the terms: 8 + 6x + x2 = 4(4 + x + 2x) + -1 Combine like terms: x + 2x = 3x 8 + 6x + x2 = 4(4 + 3x) + -1 8 + 6x + x2 = (4 * 4 + 3x * 4) + -1 8 + 6x + x2 = (16 + 12x) + -1 Reorder the terms: 8 + 6x + x2 = 16 + -1 + 12x Combine like terms: 16 + -1 = 15 8 + 6x + x2 = 15 + 12x Solving 8 + 6x + x2 = 15 + 12x Solving for variable 'x'. Reorder the terms: 8 + -15 + 6x + -12x + x2 = 15 + 12x + -15 + -12x Combine like terms: 8 + -15 = -7 -7 + 6x + -12x + x2 = 15 + 12x + -15 + -12x Combine like terms: 6x + -12x = -6x -7 + -6x + x2 = 15 + 12x + -15 + -12x Reorder the terms: -7 + -6x + x2 = 15 + -15 + 12x + -12x Combine like terms: 15 + -15 = 0 -7 + -6x + x2 = 0 + 12x + -12x -7 + -6x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -7 + -6x + x2 = 0 Factor a trinomial. (-1 + -1x)(7 + -1x) = 0Subproblem 1
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 = -1Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-1, 7}
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