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Simplifying x(x2 + 19) + 6 = (2x + 3)(3x + 2) + -1x2 Reorder the terms: x(19 + x2) + 6 = (2x + 3)(3x + 2) + -1x2 (19 * x + x2 * x) + 6 = (2x + 3)(3x + 2) + -1x2 (19x + x3) + 6 = (2x + 3)(3x + 2) + -1x2 Reorder the terms: 6 + 19x + x3 = (2x + 3)(3x + 2) + -1x2 Reorder the terms: 6 + 19x + x3 = (3 + 2x)(3x + 2) + -1x2 Reorder the terms: 6 + 19x + x3 = (3 + 2x)(2 + 3x) + -1x2 Multiply (3 + 2x) * (2 + 3x) 6 + 19x + x3 = (3(2 + 3x) + 2x * (2 + 3x)) + -1x2 6 + 19x + x3 = ((2 * 3 + 3x * 3) + 2x * (2 + 3x)) + -1x2 6 + 19x + x3 = ((6 + 9x) + 2x * (2 + 3x)) + -1x2 6 + 19x + x3 = (6 + 9x + (2 * 2x + 3x * 2x)) + -1x2 6 + 19x + x3 = (6 + 9x + (4x + 6x2)) + -1x2 Combine like terms: 9x + 4x = 13x 6 + 19x + x3 = (6 + 13x + 6x2) + -1x2 Combine like terms: 6x2 + -1x2 = 5x2 6 + 19x + x3 = 6 + 13x + 5x2 Add '-6' to each side of the equation. 6 + 19x + -6 + x3 = 6 + 13x + -6 + 5x2 Reorder the terms: 6 + -6 + 19x + x3 = 6 + 13x + -6 + 5x2 Combine like terms: 6 + -6 = 0 0 + 19x + x3 = 6 + 13x + -6 + 5x2 19x + x3 = 6 + 13x + -6 + 5x2 Reorder the terms: 19x + x3 = 6 + -6 + 13x + 5x2 Combine like terms: 6 + -6 = 0 19x + x3 = 0 + 13x + 5x2 19x + x3 = 13x + 5x2 Solving 19x + x3 = 13x + 5x2 Solving for variable 'x'. Reorder the terms: 19x + -13x + -5x2 + x3 = 13x + 5x2 + -13x + -5x2 Combine like terms: 19x + -13x = 6x 6x + -5x2 + x3 = 13x + 5x2 + -13x + -5x2 Reorder the terms: 6x + -5x2 + x3 = 13x + -13x + 5x2 + -5x2 Combine like terms: 13x + -13x = 0 6x + -5x2 + x3 = 0 + 5x2 + -5x2 6x + -5x2 + x3 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 6x + -5x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(6 + -5x + x2) = 0 Factor a trinomial. x((2 + -1x)(3 + -1x)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {0, 2, 3}
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