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Simplifying (x + 4)(x + a) = x2 + 7x + 12 Reorder the terms: (4 + x)(x + a) = x2 + 7x + 12 Reorder the terms: (4 + x)(a + x) = x2 + 7x + 12 Multiply (4 + x) * (a + x) (4(a + x) + x(a + x)) = x2 + 7x + 12 ((a * 4 + x * 4) + x(a + x)) = x2 + 7x + 12 ((4a + 4x) + x(a + x)) = x2 + 7x + 12 (4a + 4x + (a * x + x * x)) = x2 + 7x + 12 (4a + 4x + (ax + x2)) = x2 + 7x + 12 Reorder the terms: (4a + ax + 4x + x2) = x2 + 7x + 12 (4a + ax + 4x + x2) = x2 + 7x + 12 Reorder the terms: 4a + ax + 4x + x2 = 12 + 7x + x2 Add '-1x2' to each side of the equation. 4a + ax + 4x + x2 + -1x2 = 12 + 7x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4a + ax + 4x + 0 = 12 + 7x + x2 + -1x2 4a + ax + 4x = 12 + 7x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 4a + ax + 4x = 12 + 7x + 0 4a + ax + 4x = 12 + 7x Solving 4a + ax + 4x = 12 + 7x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4x' to each side of the equation. 4a + ax + 4x + -4x = 12 + 7x + -4x Combine like terms: 4x + -4x = 0 4a + ax + 0 = 12 + 7x + -4x 4a + ax = 12 + 7x + -4x Combine like terms: 7x + -4x = 3x 4a + ax = 12 + 3x Reorder the terms: -12 + 4a + ax + -3x = 12 + 3x + -12 + -3x Reorder the terms: -12 + 4a + ax + -3x = 12 + -12 + 3x + -3x Combine like terms: 12 + -12 = 0 -12 + 4a + ax + -3x = 0 + 3x + -3x -12 + 4a + ax + -3x = 3x + -3x Combine like terms: 3x + -3x = 0 -12 + 4a + ax + -3x = 0 The solution to this equation could not be determined.
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