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Simplifying (2x + 3)(2 + -3x) + -1(2 + -3x)(4x + 1) = 0 Reorder the terms: (3 + 2x)(2 + -3x) + -1(2 + -3x)(4x + 1) = 0 Multiply (3 + 2x) * (2 + -3x) (3(2 + -3x) + 2x * (2 + -3x)) + -1(2 + -3x)(4x + 1) = 0 ((2 * 3 + -3x * 3) + 2x * (2 + -3x)) + -1(2 + -3x)(4x + 1) = 0 ((6 + -9x) + 2x * (2 + -3x)) + -1(2 + -3x)(4x + 1) = 0 (6 + -9x + (2 * 2x + -3x * 2x)) + -1(2 + -3x)(4x + 1) = 0 (6 + -9x + (4x + -6x2)) + -1(2 + -3x)(4x + 1) = 0 Combine like terms: -9x + 4x = -5x (6 + -5x + -6x2) + -1(2 + -3x)(4x + 1) = 0 Reorder the terms: 6 + -5x + -6x2 + -1(2 + -3x)(1 + 4x) = 0 Multiply (2 + -3x) * (1 + 4x) 6 + -5x + -6x2 + -1(2(1 + 4x) + -3x * (1 + 4x)) = 0 6 + -5x + -6x2 + -1((1 * 2 + 4x * 2) + -3x * (1 + 4x)) = 0 6 + -5x + -6x2 + -1((2 + 8x) + -3x * (1 + 4x)) = 0 6 + -5x + -6x2 + -1(2 + 8x + (1 * -3x + 4x * -3x)) = 0 6 + -5x + -6x2 + -1(2 + 8x + (-3x + -12x2)) = 0 Combine like terms: 8x + -3x = 5x 6 + -5x + -6x2 + -1(2 + 5x + -12x2) = 0 6 + -5x + -6x2 + (2 * -1 + 5x * -1 + -12x2 * -1) = 0 6 + -5x + -6x2 + (-2 + -5x + 12x2) = 0 Reorder the terms: 6 + -2 + -5x + -5x + -6x2 + 12x2 = 0 Combine like terms: 6 + -2 = 4 4 + -5x + -5x + -6x2 + 12x2 = 0 Combine like terms: -5x + -5x = -10x 4 + -10x + -6x2 + 12x2 = 0 Combine like terms: -6x2 + 12x2 = 6x2 4 + -10x + 6x2 = 0 Solving 4 + -10x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -5x + 3x2) = 0 Factor a trinomial. 2((2 + -3x)(1 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 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 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Subproblem 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 = {0.6666666667, 1}
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