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Simplifying 2x(x + 3) = (3x + 1)(x + 1) Reorder the terms: 2x(3 + x) = (3x + 1)(x + 1) (3 * 2x + x * 2x) = (3x + 1)(x + 1) (6x + 2x2) = (3x + 1)(x + 1) Reorder the terms: 6x + 2x2 = (1 + 3x)(x + 1) Reorder the terms: 6x + 2x2 = (1 + 3x)(1 + x) Multiply (1 + 3x) * (1 + x) 6x + 2x2 = (1(1 + x) + 3x * (1 + x)) 6x + 2x2 = ((1 * 1 + x * 1) + 3x * (1 + x)) 6x + 2x2 = ((1 + 1x) + 3x * (1 + x)) 6x + 2x2 = (1 + 1x + (1 * 3x + x * 3x)) 6x + 2x2 = (1 + 1x + (3x + 3x2)) Combine like terms: 1x + 3x = 4x 6x + 2x2 = (1 + 4x + 3x2) Solving 6x + 2x2 = 1 + 4x + 3x2 Solving for variable 'x'. Reorder the terms: -1 + 6x + -4x + 2x2 + -3x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2 Combine like terms: 6x + -4x = 2x -1 + 2x + 2x2 + -3x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2 Combine like terms: 2x2 + -3x2 = -1x2 -1 + 2x + -1x2 = 1 + 4x + 3x2 + -1 + -4x + -3x2 Reorder the terms: -1 + 2x + -1x2 = 1 + -1 + 4x + -4x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 -1 + 2x + -1x2 = 0 + 4x + -4x + 3x2 + -3x2 -1 + 2x + -1x2 = 4x + -4x + 3x2 + -3x2 Combine like terms: 4x + -4x = 0 -1 + 2x + -1x2 = 0 + 3x2 + -3x2 -1 + 2x + -1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -1 + 2x + -1x2 = 0 Factor a trinomial. (-1 + x)(1 + -1x) = 0Subproblem 1
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 = 1Subproblem 2
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 = 1Solution
x = {1, 1}
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