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Simplifying (x + 1)(2x) + (x2 + 3) = (2x + 3)(2x + -3) + 9 Reorder the terms: (1 + x)(2x) + (x2 + 3) = (2x + 3)(2x + -3) + 9 Remove parenthesis around (2x) (1 + x) * 2x + (x2 + 3) = (2x + 3)(2x + -3) + 9 Reorder the terms for easier multiplication: 2x(1 + x) + (x2 + 3) = (2x + 3)(2x + -3) + 9 (1 * 2x + x * 2x) + (x2 + 3) = (2x + 3)(2x + -3) + 9 (2x + 2x2) + (x2 + 3) = (2x + 3)(2x + -3) + 9 Reorder the terms: 2x + 2x2 + (3 + x2) = (2x + 3)(2x + -3) + 9 Remove parenthesis around (3 + x2) 2x + 2x2 + 3 + x2 = (2x + 3)(2x + -3) + 9 Reorder the terms: 3 + 2x + 2x2 + x2 = (2x + 3)(2x + -3) + 9 Combine like terms: 2x2 + x2 = 3x2 3 + 2x + 3x2 = (2x + 3)(2x + -3) + 9 Reorder the terms: 3 + 2x + 3x2 = (3 + 2x)(2x + -3) + 9 Reorder the terms: 3 + 2x + 3x2 = (3 + 2x)(-3 + 2x) + 9 Multiply (3 + 2x) * (-3 + 2x) 3 + 2x + 3x2 = (3(-3 + 2x) + 2x * (-3 + 2x)) + 9 3 + 2x + 3x2 = ((-3 * 3 + 2x * 3) + 2x * (-3 + 2x)) + 9 3 + 2x + 3x2 = ((-9 + 6x) + 2x * (-3 + 2x)) + 9 3 + 2x + 3x2 = (-9 + 6x + (-3 * 2x + 2x * 2x)) + 9 3 + 2x + 3x2 = (-9 + 6x + (-6x + 4x2)) + 9 Combine like terms: 6x + -6x = 0 3 + 2x + 3x2 = (-9 + 0 + 4x2) + 9 3 + 2x + 3x2 = (-9 + 4x2) + 9 Reorder the terms: 3 + 2x + 3x2 = -9 + 9 + 4x2 Combine like terms: -9 + 9 = 0 3 + 2x + 3x2 = 0 + 4x2 3 + 2x + 3x2 = 4x2 Solving 3 + 2x + 3x2 = 4x2 Solving for variable 'x'. Combine like terms: 3x2 + -4x2 = -1x2 3 + 2x + -1x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 3 + 2x + -1x2 = 0 Factor a trinomial. (3 + -1x)(1 + x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = {3, -1}
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