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Simplifying 2 + -10x = (3x + -7)(x + 1) Reorder the terms: 2 + -10x = (-7 + 3x)(x + 1) Reorder the terms: 2 + -10x = (-7 + 3x)(1 + x) Multiply (-7 + 3x) * (1 + x) 2 + -10x = (-7(1 + x) + 3x * (1 + x)) 2 + -10x = ((1 * -7 + x * -7) + 3x * (1 + x)) 2 + -10x = ((-7 + -7x) + 3x * (1 + x)) 2 + -10x = (-7 + -7x + (1 * 3x + x * 3x)) 2 + -10x = (-7 + -7x + (3x + 3x2)) Combine like terms: -7x + 3x = -4x 2 + -10x = (-7 + -4x + 3x2) Solving 2 + -10x = -7 + -4x + 3x2 Solving for variable 'x'. Reorder the terms: 2 + 7 + -10x + 4x + -3x2 = -7 + -4x + 3x2 + 7 + 4x + -3x2 Combine like terms: 2 + 7 = 9 9 + -10x + 4x + -3x2 = -7 + -4x + 3x2 + 7 + 4x + -3x2 Combine like terms: -10x + 4x = -6x 9 + -6x + -3x2 = -7 + -4x + 3x2 + 7 + 4x + -3x2 Reorder the terms: 9 + -6x + -3x2 = -7 + 7 + -4x + 4x + 3x2 + -3x2 Combine like terms: -7 + 7 = 0 9 + -6x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2 9 + -6x + -3x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 9 + -6x + -3x2 = 0 + 3x2 + -3x2 9 + -6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 9 + -6x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(3 + -2x + -1x2) = 0 Factor a trinomial. 3((1 + -1x)(3 + x)) = 0 Ignore the factor 3.Subproblem 1
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 = 1Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {1, -3}
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