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Simplifying (2x + 2)(3x + -1) = (2x + 2)(14x + 2) Reorder the terms: (2 + 2x)(3x + -1) = (2x + 2)(14x + 2) Reorder the terms: (2 + 2x)(-1 + 3x) = (2x + 2)(14x + 2) Multiply (2 + 2x) * (-1 + 3x) (2(-1 + 3x) + 2x * (-1 + 3x)) = (2x + 2)(14x + 2) ((-1 * 2 + 3x * 2) + 2x * (-1 + 3x)) = (2x + 2)(14x + 2) ((-2 + 6x) + 2x * (-1 + 3x)) = (2x + 2)(14x + 2) (-2 + 6x + (-1 * 2x + 3x * 2x)) = (2x + 2)(14x + 2) (-2 + 6x + (-2x + 6x2)) = (2x + 2)(14x + 2) Combine like terms: 6x + -2x = 4x (-2 + 4x + 6x2) = (2x + 2)(14x + 2) Reorder the terms: -2 + 4x + 6x2 = (2 + 2x)(14x + 2) Reorder the terms: -2 + 4x + 6x2 = (2 + 2x)(2 + 14x) Multiply (2 + 2x) * (2 + 14x) -2 + 4x + 6x2 = (2(2 + 14x) + 2x * (2 + 14x)) -2 + 4x + 6x2 = ((2 * 2 + 14x * 2) + 2x * (2 + 14x)) -2 + 4x + 6x2 = ((4 + 28x) + 2x * (2 + 14x)) -2 + 4x + 6x2 = (4 + 28x + (2 * 2x + 14x * 2x)) -2 + 4x + 6x2 = (4 + 28x + (4x + 28x2)) Combine like terms: 28x + 4x = 32x -2 + 4x + 6x2 = (4 + 32x + 28x2) Solving -2 + 4x + 6x2 = 4 + 32x + 28x2 Solving for variable 'x'. Reorder the terms: -2 + -4 + 4x + -32x + 6x2 + -28x2 = 4 + 32x + 28x2 + -4 + -32x + -28x2 Combine like terms: -2 + -4 = -6 -6 + 4x + -32x + 6x2 + -28x2 = 4 + 32x + 28x2 + -4 + -32x + -28x2 Combine like terms: 4x + -32x = -28x -6 + -28x + 6x2 + -28x2 = 4 + 32x + 28x2 + -4 + -32x + -28x2 Combine like terms: 6x2 + -28x2 = -22x2 -6 + -28x + -22x2 = 4 + 32x + 28x2 + -4 + -32x + -28x2 Reorder the terms: -6 + -28x + -22x2 = 4 + -4 + 32x + -32x + 28x2 + -28x2 Combine like terms: 4 + -4 = 0 -6 + -28x + -22x2 = 0 + 32x + -32x + 28x2 + -28x2 -6 + -28x + -22x2 = 32x + -32x + 28x2 + -28x2 Combine like terms: 32x + -32x = 0 -6 + -28x + -22x2 = 0 + 28x2 + -28x2 -6 + -28x + -22x2 = 28x2 + -28x2 Combine like terms: 28x2 + -28x2 = 0 -6 + -28x + -22x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 14x + 11x2) = 0 Factor a trinomial. -2((1 + x)(3 + 11x)) = 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 + 11x)' equal to zero and attempt to solve: Simplifying 3 + 11x = 0 Solving 3 + 11x = 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 + 11x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 11x = 0 + -3 11x = 0 + -3 Combine like terms: 0 + -3 = -3 11x = -3 Divide each side by '11'. x = -0.2727272727 Simplifying x = -0.2727272727Solution
x = {-1, -0.2727272727}
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