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Simplifying (3x + 2)(x + 1) = (3x + -2)(5x + -4) Reorder the terms: (2 + 3x)(x + 1) = (3x + -2)(5x + -4) Reorder the terms: (2 + 3x)(1 + x) = (3x + -2)(5x + -4) Multiply (2 + 3x) * (1 + x) (2(1 + x) + 3x * (1 + x)) = (3x + -2)(5x + -4) ((1 * 2 + x * 2) + 3x * (1 + x)) = (3x + -2)(5x + -4) ((2 + 2x) + 3x * (1 + x)) = (3x + -2)(5x + -4) (2 + 2x + (1 * 3x + x * 3x)) = (3x + -2)(5x + -4) (2 + 2x + (3x + 3x2)) = (3x + -2)(5x + -4) Combine like terms: 2x + 3x = 5x (2 + 5x + 3x2) = (3x + -2)(5x + -4) Reorder the terms: 2 + 5x + 3x2 = (-2 + 3x)(5x + -4) Reorder the terms: 2 + 5x + 3x2 = (-2 + 3x)(-4 + 5x) Multiply (-2 + 3x) * (-4 + 5x) 2 + 5x + 3x2 = (-2(-4 + 5x) + 3x * (-4 + 5x)) 2 + 5x + 3x2 = ((-4 * -2 + 5x * -2) + 3x * (-4 + 5x)) 2 + 5x + 3x2 = ((8 + -10x) + 3x * (-4 + 5x)) 2 + 5x + 3x2 = (8 + -10x + (-4 * 3x + 5x * 3x)) 2 + 5x + 3x2 = (8 + -10x + (-12x + 15x2)) Combine like terms: -10x + -12x = -22x 2 + 5x + 3x2 = (8 + -22x + 15x2) Solving 2 + 5x + 3x2 = 8 + -22x + 15x2 Solving for variable 'x'. Reorder the terms: 2 + -8 + 5x + 22x + 3x2 + -15x2 = 8 + -22x + 15x2 + -8 + 22x + -15x2 Combine like terms: 2 + -8 = -6 -6 + 5x + 22x + 3x2 + -15x2 = 8 + -22x + 15x2 + -8 + 22x + -15x2 Combine like terms: 5x + 22x = 27x -6 + 27x + 3x2 + -15x2 = 8 + -22x + 15x2 + -8 + 22x + -15x2 Combine like terms: 3x2 + -15x2 = -12x2 -6 + 27x + -12x2 = 8 + -22x + 15x2 + -8 + 22x + -15x2 Reorder the terms: -6 + 27x + -12x2 = 8 + -8 + -22x + 22x + 15x2 + -15x2 Combine like terms: 8 + -8 = 0 -6 + 27x + -12x2 = 0 + -22x + 22x + 15x2 + -15x2 -6 + 27x + -12x2 = -22x + 22x + 15x2 + -15x2 Combine like terms: -22x + 22x = 0 -6 + 27x + -12x2 = 0 + 15x2 + -15x2 -6 + 27x + -12x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 -6 + 27x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 9x + -4x2) = 0 Factor a trinomial. 3((-2 + x)(1 + -4x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Subproblem 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 = {2, 0.25}
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