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Simplifying 6x2 + x + a = (6x + a)(x + 1) Reorder the terms: a + x + 6x2 = (6x + a)(x + 1) Reorder the terms: a + x + 6x2 = (a + 6x)(x + 1) Reorder the terms: a + x + 6x2 = (a + 6x)(1 + x) Multiply (a + 6x) * (1 + x) a + x + 6x2 = (a(1 + x) + 6x * (1 + x)) a + x + 6x2 = ((1 * a + x * a) + 6x * (1 + x)) a + x + 6x2 = ((1a + ax) + 6x * (1 + x)) a + x + 6x2 = (1a + ax + (1 * 6x + x * 6x)) a + x + 6x2 = (1a + ax + (6x + 6x2)) a + x + 6x2 = (1a + ax + 6x + 6x2) Add '-6x2' to each side of the equation. a + x + 6x2 + -6x2 = 1a + ax + 6x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 a + x + 0 = 1a + ax + 6x + 6x2 + -6x2 a + x = 1a + ax + 6x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 a + x = 1a + ax + 6x + 0 a + x = 1a + ax + 6x Solving a + x = 1a + ax + 6x Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1a' to each side of the equation. a + -1a + x = 1a + ax + -1a + 6x Combine like terms: a + -1a = 0 0 + x = 1a + ax + -1a + 6x x = 1a + ax + -1a + 6x Reorder the terms: x = 1a + -1a + ax + 6x Combine like terms: 1a + -1a = 0 x = 0 + ax + 6x x = ax + 6x Add '-1ax' to each side of the equation. -1ax + x = ax + -1ax + 6x Combine like terms: ax + -1ax = 0 -1ax + x = 0 + 6x -1ax + x = 6x Add '-1x' to each side of the equation. -1ax + x + -1x = 6x + -1x Combine like terms: x + -1x = 0 -1ax + 0 = 6x + -1x -1ax = 6x + -1x Combine like terms: 6x + -1x = 5x -1ax = 5x Divide each side by '-1x'. a = -5 Simplifying a = -5
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