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Simplifying (x2 + 5x + 6)(x + -1) = (x2 + 8x + 16)(x + -4) + 7 Reorder the terms: (6 + 5x + x2)(x + -1) = (x2 + 8x + 16)(x + -4) + 7 Reorder the terms: (6 + 5x + x2)(-1 + x) = (x2 + 8x + 16)(x + -4) + 7 Multiply (6 + 5x + x2) * (-1 + x) (6(-1 + x) + 5x * (-1 + x) + x2(-1 + x)) = (x2 + 8x + 16)(x + -4) + 7 ((-1 * 6 + x * 6) + 5x * (-1 + x) + x2(-1 + x)) = (x2 + 8x + 16)(x + -4) + 7 ((-6 + 6x) + 5x * (-1 + x) + x2(-1 + x)) = (x2 + 8x + 16)(x + -4) + 7 (-6 + 6x + (-1 * 5x + x * 5x) + x2(-1 + x)) = (x2 + 8x + 16)(x + -4) + 7 (-6 + 6x + (-5x + 5x2) + x2(-1 + x)) = (x2 + 8x + 16)(x + -4) + 7 (-6 + 6x + -5x + 5x2 + (-1 * x2 + x * x2)) = (x2 + 8x + 16)(x + -4) + 7 (-6 + 6x + -5x + 5x2 + (-1x2 + x3)) = (x2 + 8x + 16)(x + -4) + 7 Combine like terms: 6x + -5x = 1x (-6 + 1x + 5x2 + -1x2 + x3) = (x2 + 8x + 16)(x + -4) + 7 Combine like terms: 5x2 + -1x2 = 4x2 (-6 + 1x + 4x2 + x3) = (x2 + 8x + 16)(x + -4) + 7 Reorder the terms: -6 + 1x + 4x2 + x3 = (16 + 8x + x2)(x + -4) + 7 Reorder the terms: -6 + 1x + 4x2 + x3 = (16 + 8x + x2)(-4 + x) + 7 Multiply (16 + 8x + x2) * (-4 + x) -6 + 1x + 4x2 + x3 = (16(-4 + x) + 8x * (-4 + x) + x2(-4 + x)) + 7 -6 + 1x + 4x2 + x3 = ((-4 * 16 + x * 16) + 8x * (-4 + x) + x2(-4 + x)) + 7 -6 + 1x + 4x2 + x3 = ((-64 + 16x) + 8x * (-4 + x) + x2(-4 + x)) + 7 -6 + 1x + 4x2 + x3 = (-64 + 16x + (-4 * 8x + x * 8x) + x2(-4 + x)) + 7 -6 + 1x + 4x2 + x3 = (-64 + 16x + (-32x + 8x2) + x2(-4 + x)) + 7 -6 + 1x + 4x2 + x3 = (-64 + 16x + -32x + 8x2 + (-4 * x2 + x * x2)) + 7 -6 + 1x + 4x2 + x3 = (-64 + 16x + -32x + 8x2 + (-4x2 + x3)) + 7 Combine like terms: 16x + -32x = -16x -6 + 1x + 4x2 + x3 = (-64 + -16x + 8x2 + -4x2 + x3) + 7 Combine like terms: 8x2 + -4x2 = 4x2 -6 + 1x + 4x2 + x3 = (-64 + -16x + 4x2 + x3) + 7 Reorder the terms: -6 + 1x + 4x2 + x3 = -64 + 7 + -16x + 4x2 + x3 Combine like terms: -64 + 7 = -57 -6 + 1x + 4x2 + x3 = -57 + -16x + 4x2 + x3 Add '-4x2' to each side of the equation. -6 + 1x + 4x2 + -4x2 + x3 = -57 + -16x + 4x2 + -4x2 + x3 Combine like terms: 4x2 + -4x2 = 0 -6 + 1x + 0 + x3 = -57 + -16x + 4x2 + -4x2 + x3 -6 + 1x + x3 = -57 + -16x + 4x2 + -4x2 + x3 Combine like terms: 4x2 + -4x2 = 0 -6 + 1x + x3 = -57 + -16x + 0 + x3 -6 + 1x + x3 = -57 + -16x + x3 Add '-1x3' to each side of the equation. -6 + 1x + x3 + -1x3 = -57 + -16x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -6 + 1x + 0 = -57 + -16x + x3 + -1x3 -6 + 1x = -57 + -16x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 -6 + 1x = -57 + -16x + 0 -6 + 1x = -57 + -16x Solving -6 + 1x = -57 + -16x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16x' to each side of the equation. -6 + 1x + 16x = -57 + -16x + 16x Combine like terms: 1x + 16x = 17x -6 + 17x = -57 + -16x + 16x Combine like terms: -16x + 16x = 0 -6 + 17x = -57 + 0 -6 + 17x = -57 Add '6' to each side of the equation. -6 + 6 + 17x = -57 + 6 Combine like terms: -6 + 6 = 0 0 + 17x = -57 + 6 17x = -57 + 6 Combine like terms: -57 + 6 = -51 17x = -51 Divide each side by '17'. x = -3 Simplifying x = -3
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