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Simplifying (4x + -2)(x + 7) + -1(x + 7)(2x + -4) = 0 Reorder the terms: (-2 + 4x)(x + 7) + -1(x + 7)(2x + -4) = 0 Reorder the terms: (-2 + 4x)(7 + x) + -1(x + 7)(2x + -4) = 0 Multiply (-2 + 4x) * (7 + x) (-2(7 + x) + 4x * (7 + x)) + -1(x + 7)(2x + -4) = 0 ((7 * -2 + x * -2) + 4x * (7 + x)) + -1(x + 7)(2x + -4) = 0 ((-14 + -2x) + 4x * (7 + x)) + -1(x + 7)(2x + -4) = 0 (-14 + -2x + (7 * 4x + x * 4x)) + -1(x + 7)(2x + -4) = 0 (-14 + -2x + (28x + 4x2)) + -1(x + 7)(2x + -4) = 0 Combine like terms: -2x + 28x = 26x (-14 + 26x + 4x2) + -1(x + 7)(2x + -4) = 0 Reorder the terms: -14 + 26x + 4x2 + -1(7 + x)(2x + -4) = 0 Reorder the terms: -14 + 26x + 4x2 + -1(7 + x)(-4 + 2x) = 0 Multiply (7 + x) * (-4 + 2x) -14 + 26x + 4x2 + -1(7(-4 + 2x) + x(-4 + 2x)) = 0 -14 + 26x + 4x2 + -1((-4 * 7 + 2x * 7) + x(-4 + 2x)) = 0 -14 + 26x + 4x2 + -1((-28 + 14x) + x(-4 + 2x)) = 0 -14 + 26x + 4x2 + -1(-28 + 14x + (-4 * x + 2x * x)) = 0 -14 + 26x + 4x2 + -1(-28 + 14x + (-4x + 2x2)) = 0 Combine like terms: 14x + -4x = 10x -14 + 26x + 4x2 + -1(-28 + 10x + 2x2) = 0 -14 + 26x + 4x2 + (-28 * -1 + 10x * -1 + 2x2 * -1) = 0 -14 + 26x + 4x2 + (28 + -10x + -2x2) = 0 Reorder the terms: -14 + 28 + 26x + -10x + 4x2 + -2x2 = 0 Combine like terms: -14 + 28 = 14 14 + 26x + -10x + 4x2 + -2x2 = 0 Combine like terms: 26x + -10x = 16x 14 + 16x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 14 + 16x + 2x2 = 0 Solving 14 + 16x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 8x + x2) = 0 Factor a trinomial. 2((7 + x)(1 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7Subproblem 2
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 = -1Solution
x = {-7, -1}
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