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Simplifying 2x(x + 3) = (3x + 1)(x + 3) Reorder the terms: 2x(3 + x) = (3x + 1)(x + 3) (3 * 2x + x * 2x) = (3x + 1)(x + 3) (6x + 2x2) = (3x + 1)(x + 3) Reorder the terms: 6x + 2x2 = (1 + 3x)(x + 3) Reorder the terms: 6x + 2x2 = (1 + 3x)(3 + x) Multiply (1 + 3x) * (3 + x) 6x + 2x2 = (1(3 + x) + 3x * (3 + x)) 6x + 2x2 = ((3 * 1 + x * 1) + 3x * (3 + x)) 6x + 2x2 = ((3 + 1x) + 3x * (3 + x)) 6x + 2x2 = (3 + 1x + (3 * 3x + x * 3x)) 6x + 2x2 = (3 + 1x + (9x + 3x2)) Combine like terms: 1x + 9x = 10x 6x + 2x2 = (3 + 10x + 3x2) Solving 6x + 2x2 = 3 + 10x + 3x2 Solving for variable 'x'. Reorder the terms: -3 + 6x + -10x + 2x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Combine like terms: 6x + -10x = -4x -3 + -4x + 2x2 + -3x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 -3 + -4x + -1x2 = 3 + 10x + 3x2 + -3 + -10x + -3x2 Reorder the terms: -3 + -4x + -1x2 = 3 + -3 + 10x + -10x + 3x2 + -3x2 Combine like terms: 3 + -3 = 0 -3 + -4x + -1x2 = 0 + 10x + -10x + 3x2 + -3x2 -3 + -4x + -1x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 -3 + -4x + -1x2 = 0 + 3x2 + -3x2 -3 + -4x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -3 + -4x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 4x + x2) = 0 Factor a trinomial. -1((3 + x)(1 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 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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