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Simplifying x(x + -2) + (x + -2) + -1(x + -2)(7x + 9) = 0 Reorder the terms: x(-2 + x) + (x + -2) + -1(x + -2)(7x + 9) = 0 (-2 * x + x * x) + (x + -2) + -1(x + -2)(7x + 9) = 0 (-2x + x2) + (x + -2) + -1(x + -2)(7x + 9) = 0 Reorder the terms: -2x + x2 + (-2 + x) + -1(x + -2)(7x + 9) = 0 Remove parenthesis around (-2 + x) -2x + x2 + -2 + x + -1(x + -2)(7x + 9) = 0 Reorder the terms: -2x + x2 + -2 + x + -1(-2 + x)(7x + 9) = 0 Reorder the terms: -2x + x2 + -2 + x + -1(-2 + x)(9 + 7x) = 0 Multiply (-2 + x) * (9 + 7x) -2x + x2 + -2 + x + -1(-2(9 + 7x) + x(9 + 7x)) = 0 -2x + x2 + -2 + x + -1((9 * -2 + 7x * -2) + x(9 + 7x)) = 0 -2x + x2 + -2 + x + -1((-18 + -14x) + x(9 + 7x)) = 0 -2x + x2 + -2 + x + -1(-18 + -14x + (9 * x + 7x * x)) = 0 -2x + x2 + -2 + x + -1(-18 + -14x + (9x + 7x2)) = 0 Combine like terms: -14x + 9x = -5x -2x + x2 + -2 + x + -1(-18 + -5x + 7x2) = 0 -2x + x2 + -2 + x + (-18 * -1 + -5x * -1 + 7x2 * -1) = 0 -2x + x2 + -2 + x + (18 + 5x + -7x2) = 0 Reorder the terms: -2 + 18 + -2x + x + 5x + x2 + -7x2 = 0 Combine like terms: -2 + 18 = 16 16 + -2x + x + 5x + x2 + -7x2 = 0 Combine like terms: -2x + x = -1x 16 + -1x + 5x + x2 + -7x2 = 0 Combine like terms: -1x + 5x = 4x 16 + 4x + x2 + -7x2 = 0 Combine like terms: x2 + -7x2 = -6x2 16 + 4x + -6x2 = 0 Solving 16 + 4x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 2x + -3x2) = 0 Factor a trinomial. 2((2 + -1x)(4 + 3x)) = 0 Ignore the factor 2.Subproblem 1
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 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve: Simplifying 4 + 3x = 0 Solving 4 + 3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x = 0 + -4 3x = 0 + -4 Combine like terms: 0 + -4 = -4 3x = -4 Divide each side by '3'. x = -1.333333333 Simplifying x = -1.333333333Solution
x = {2, -1.333333333}
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