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Simplifying (x + -4)(x + 7) + -1(2x + 3)(x + 7) = 0 Reorder the terms: (-4 + x)(x + 7) + -1(2x + 3)(x + 7) = 0 Reorder the terms: (-4 + x)(7 + x) + -1(2x + 3)(x + 7) = 0 Multiply (-4 + x) * (7 + x) (-4(7 + x) + x(7 + x)) + -1(2x + 3)(x + 7) = 0 ((7 * -4 + x * -4) + x(7 + x)) + -1(2x + 3)(x + 7) = 0 ((-28 + -4x) + x(7 + x)) + -1(2x + 3)(x + 7) = 0 (-28 + -4x + (7 * x + x * x)) + -1(2x + 3)(x + 7) = 0 (-28 + -4x + (7x + x2)) + -1(2x + 3)(x + 7) = 0 Combine like terms: -4x + 7x = 3x (-28 + 3x + x2) + -1(2x + 3)(x + 7) = 0 Reorder the terms: -28 + 3x + x2 + -1(3 + 2x)(x + 7) = 0 Reorder the terms: -28 + 3x + x2 + -1(3 + 2x)(7 + x) = 0 Multiply (3 + 2x) * (7 + x) -28 + 3x + x2 + -1(3(7 + x) + 2x * (7 + x)) = 0 -28 + 3x + x2 + -1((7 * 3 + x * 3) + 2x * (7 + x)) = 0 -28 + 3x + x2 + -1((21 + 3x) + 2x * (7 + x)) = 0 -28 + 3x + x2 + -1(21 + 3x + (7 * 2x + x * 2x)) = 0 -28 + 3x + x2 + -1(21 + 3x + (14x + 2x2)) = 0 Combine like terms: 3x + 14x = 17x -28 + 3x + x2 + -1(21 + 17x + 2x2) = 0 -28 + 3x + x2 + (21 * -1 + 17x * -1 + 2x2 * -1) = 0 -28 + 3x + x2 + (-21 + -17x + -2x2) = 0 Reorder the terms: -28 + -21 + 3x + -17x + x2 + -2x2 = 0 Combine like terms: -28 + -21 = -49 -49 + 3x + -17x + x2 + -2x2 = 0 Combine like terms: 3x + -17x = -14x -49 + -14x + x2 + -2x2 = 0 Combine like terms: x2 + -2x2 = -1x2 -49 + -14x + -1x2 = 0 Solving -49 + -14x + -1x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(49 + 14x + x2) = 0 Factor a trinomial. -1((7 + x)(7 + x)) = 0 Ignore the factor -1.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 '(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 = -7Solution
x = {-7, -7}
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