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Simplifying 3(x + x + 1 + x + 2) = (x + 1)(x + 2) Reorder the terms: 3(1 + 2 + x + x + x) = (x + 1)(x + 2) Combine like terms: 1 + 2 = 3 3(3 + x + x + x) = (x + 1)(x + 2) Combine like terms: x + x = 2x 3(3 + 2x + x) = (x + 1)(x + 2) Combine like terms: 2x + x = 3x 3(3 + 3x) = (x + 1)(x + 2) (3 * 3 + 3x * 3) = (x + 1)(x + 2) (9 + 9x) = (x + 1)(x + 2) Reorder the terms: 9 + 9x = (1 + x)(x + 2) Reorder the terms: 9 + 9x = (1 + x)(2 + x) Multiply (1 + x) * (2 + x) 9 + 9x = (1(2 + x) + x(2 + x)) 9 + 9x = ((2 * 1 + x * 1) + x(2 + x)) 9 + 9x = ((2 + 1x) + x(2 + x)) 9 + 9x = (2 + 1x + (2 * x + x * x)) 9 + 9x = (2 + 1x + (2x + x2)) Combine like terms: 1x + 2x = 3x 9 + 9x = (2 + 3x + x2) Solving 9 + 9x = 2 + 3x + x2 Solving for variable 'x'. Reorder the terms: 9 + -2 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Combine like terms: 9 + -2 = 7 7 + 9x + -3x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Combine like terms: 9x + -3x = 6x 7 + 6x + -1x2 = 2 + 3x + x2 + -2 + -3x + -1x2 Reorder the terms: 7 + 6x + -1x2 = 2 + -2 + 3x + -3x + x2 + -1x2 Combine like terms: 2 + -2 = 0 7 + 6x + -1x2 = 0 + 3x + -3x + x2 + -1x2 7 + 6x + -1x2 = 3x + -3x + x2 + -1x2 Combine like terms: 3x + -3x = 0 7 + 6x + -1x2 = 0 + x2 + -1x2 7 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 7 + 6x + -1x2 = 0 Factor a trinomial. (7 + -1x)(1 + x) = 0Subproblem 1
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 = 7Subproblem 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 = {7, -1}
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