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Simplifying (2x)(x + 1) = (3x + -1)(2x + -3) Remove parenthesis around (2x) 2x(x + 1) = (3x + -1)(2x + -3) Reorder the terms: 2x(1 + x) = (3x + -1)(2x + -3) (1 * 2x + x * 2x) = (3x + -1)(2x + -3) (2x + 2x2) = (3x + -1)(2x + -3) Reorder the terms: 2x + 2x2 = (-1 + 3x)(2x + -3) Reorder the terms: 2x + 2x2 = (-1 + 3x)(-3 + 2x) Multiply (-1 + 3x) * (-3 + 2x) 2x + 2x2 = (-1(-3 + 2x) + 3x * (-3 + 2x)) 2x + 2x2 = ((-3 * -1 + 2x * -1) + 3x * (-3 + 2x)) 2x + 2x2 = ((3 + -2x) + 3x * (-3 + 2x)) 2x + 2x2 = (3 + -2x + (-3 * 3x + 2x * 3x)) 2x + 2x2 = (3 + -2x + (-9x + 6x2)) Combine like terms: -2x + -9x = -11x 2x + 2x2 = (3 + -11x + 6x2) Solving 2x + 2x2 = 3 + -11x + 6x2 Solving for variable 'x'. Reorder the terms: -3 + 2x + 11x + 2x2 + -6x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2 Combine like terms: 2x + 11x = 13x -3 + 13x + 2x2 + -6x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2 Combine like terms: 2x2 + -6x2 = -4x2 -3 + 13x + -4x2 = 3 + -11x + 6x2 + -3 + 11x + -6x2 Reorder the terms: -3 + 13x + -4x2 = 3 + -3 + -11x + 11x + 6x2 + -6x2 Combine like terms: 3 + -3 = 0 -3 + 13x + -4x2 = 0 + -11x + 11x + 6x2 + -6x2 -3 + 13x + -4x2 = -11x + 11x + 6x2 + -6x2 Combine like terms: -11x + 11x = 0 -3 + 13x + -4x2 = 0 + 6x2 + -6x2 -3 + 13x + -4x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -3 + 13x + -4x2 = 0 Factor a trinomial. (-3 + x)(1 + -4x) = 0Subproblem 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 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 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 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Divide each side by '-4'. x = 0.25 Simplifying x = 0.25Solution
x = {3, 0.25}
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