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Simplifying 2x3 + -2x(x + -3)(x + 3) + 4x = 14 + -1(2x + -4)(2x + -4) Reorder the terms: 2x3 + -2x(-3 + x)(x + 3) + 4x = 14 + -1(2x + -4)(2x + -4) Reorder the terms: 2x3 + -2x(-3 + x)(3 + x) + 4x = 14 + -1(2x + -4)(2x + -4) Multiply (-3 + x) * (3 + x) 2x3 + -2x(-3(3 + x) + x(3 + x)) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + -2x((3 * -3 + x * -3) + x(3 + x)) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + -2x((-9 + -3x) + x(3 + x)) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + -2x(-9 + -3x + (3 * x + x * x)) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + -2x(-9 + -3x + (3x + x2)) + 4x = 14 + -1(2x + -4)(2x + -4) Combine like terms: -3x + 3x = 0 2x3 + -2x(-9 + 0 + x2) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + -2x(-9 + x2) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + (-9 * -2x + x2 * -2x) + 4x = 14 + -1(2x + -4)(2x + -4) 2x3 + (18x + -2x3) + 4x = 14 + -1(2x + -4)(2x + -4) Reorder the terms: 18x + 4x + 2x3 + -2x3 = 14 + -1(2x + -4)(2x + -4) Combine like terms: 18x + 4x = 22x 22x + 2x3 + -2x3 = 14 + -1(2x + -4)(2x + -4) Combine like terms: 2x3 + -2x3 = 0 22x + 0 = 14 + -1(2x + -4)(2x + -4) 22x = 14 + -1(2x + -4)(2x + -4) Reorder the terms: 22x = 14 + -1(-4 + 2x)(2x + -4) Reorder the terms: 22x = 14 + -1(-4 + 2x)(-4 + 2x) Multiply (-4 + 2x) * (-4 + 2x) 22x = 14 + -1(-4(-4 + 2x) + 2x * (-4 + 2x)) 22x = 14 + -1((-4 * -4 + 2x * -4) + 2x * (-4 + 2x)) 22x = 14 + -1((16 + -8x) + 2x * (-4 + 2x)) 22x = 14 + -1(16 + -8x + (-4 * 2x + 2x * 2x)) 22x = 14 + -1(16 + -8x + (-8x + 4x2)) Combine like terms: -8x + -8x = -16x 22x = 14 + -1(16 + -16x + 4x2) 22x = 14 + (16 * -1 + -16x * -1 + 4x2 * -1) 22x = 14 + (-16 + 16x + -4x2) Combine like terms: 14 + -16 = -2 22x = -2 + 16x + -4x2 Solving 22x = -2 + 16x + -4x2 Solving for variable 'x'. Reorder the terms: 2 + 22x + -16x + 4x2 = -2 + 16x + -4x2 + 2 + -16x + 4x2 Combine like terms: 22x + -16x = 6x 2 + 6x + 4x2 = -2 + 16x + -4x2 + 2 + -16x + 4x2 Reorder the terms: 2 + 6x + 4x2 = -2 + 2 + 16x + -16x + -4x2 + 4x2 Combine like terms: -2 + 2 = 0 2 + 6x + 4x2 = 0 + 16x + -16x + -4x2 + 4x2 2 + 6x + 4x2 = 16x + -16x + -4x2 + 4x2 Combine like terms: 16x + -16x = 0 2 + 6x + 4x2 = 0 + -4x2 + 4x2 2 + 6x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 2 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 3x + 2x2) = 0 Factor a trinomial. 2((1 + x)(1 + 2x)) = 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 '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 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 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-1, -0.5}
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