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Simplifying (7x + -3) = (7x + -3)(2x + -1) Reorder the terms: (-3 + 7x) = (7x + -3)(2x + -1) Remove parenthesis around (-3 + 7x) -3 + 7x = (7x + -3)(2x + -1) Reorder the terms: -3 + 7x = (-3 + 7x)(2x + -1) Reorder the terms: -3 + 7x = (-3 + 7x)(-1 + 2x) Multiply (-3 + 7x) * (-1 + 2x) -3 + 7x = (-3(-1 + 2x) + 7x * (-1 + 2x)) -3 + 7x = ((-1 * -3 + 2x * -3) + 7x * (-1 + 2x)) -3 + 7x = ((3 + -6x) + 7x * (-1 + 2x)) -3 + 7x = (3 + -6x + (-1 * 7x + 2x * 7x)) -3 + 7x = (3 + -6x + (-7x + 14x2)) Combine like terms: -6x + -7x = -13x -3 + 7x = (3 + -13x + 14x2) Solving -3 + 7x = 3 + -13x + 14x2 Solving for variable 'x'. Reorder the terms: -3 + -3 + 7x + 13x + -14x2 = 3 + -13x + 14x2 + -3 + 13x + -14x2 Combine like terms: -3 + -3 = -6 -6 + 7x + 13x + -14x2 = 3 + -13x + 14x2 + -3 + 13x + -14x2 Combine like terms: 7x + 13x = 20x -6 + 20x + -14x2 = 3 + -13x + 14x2 + -3 + 13x + -14x2 Reorder the terms: -6 + 20x + -14x2 = 3 + -3 + -13x + 13x + 14x2 + -14x2 Combine like terms: 3 + -3 = 0 -6 + 20x + -14x2 = 0 + -13x + 13x + 14x2 + -14x2 -6 + 20x + -14x2 = -13x + 13x + 14x2 + -14x2 Combine like terms: -13x + 13x = 0 -6 + 20x + -14x2 = 0 + 14x2 + -14x2 -6 + 20x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -6 + 20x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 10x + -7x2) = 0 Factor a trinomial. 2((-1 + x)(3 + -7x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve: Simplifying 3 + -7x = 0 Solving 3 + -7x = 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 + -7x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7x = 0 + -3 -7x = 0 + -3 Combine like terms: 0 + -3 = -3 -7x = -3 Divide each side by '-7'. x = 0.4285714286 Simplifying x = 0.4285714286Solution
x = {1, 0.4285714286}
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