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Simplifying x(3x + -3) + x(6x + -6) = (9x + 1)(x + -1) Reorder the terms: x(-3 + 3x) + x(6x + -6) = (9x + 1)(x + -1) (-3 * x + 3x * x) + x(6x + -6) = (9x + 1)(x + -1) (-3x + 3x2) + x(6x + -6) = (9x + 1)(x + -1) Reorder the terms: -3x + 3x2 + x(-6 + 6x) = (9x + 1)(x + -1) -3x + 3x2 + (-6 * x + 6x * x) = (9x + 1)(x + -1) -3x + 3x2 + (-6x + 6x2) = (9x + 1)(x + -1) Reorder the terms: -3x + -6x + 3x2 + 6x2 = (9x + 1)(x + -1) Combine like terms: -3x + -6x = -9x -9x + 3x2 + 6x2 = (9x + 1)(x + -1) Combine like terms: 3x2 + 6x2 = 9x2 -9x + 9x2 = (9x + 1)(x + -1) Reorder the terms: -9x + 9x2 = (1 + 9x)(x + -1) Reorder the terms: -9x + 9x2 = (1 + 9x)(-1 + x) Multiply (1 + 9x) * (-1 + x) -9x + 9x2 = (1(-1 + x) + 9x * (-1 + x)) -9x + 9x2 = ((-1 * 1 + x * 1) + 9x * (-1 + x)) -9x + 9x2 = ((-1 + 1x) + 9x * (-1 + x)) -9x + 9x2 = (-1 + 1x + (-1 * 9x + x * 9x)) -9x + 9x2 = (-1 + 1x + (-9x + 9x2)) Combine like terms: 1x + -9x = -8x -9x + 9x2 = (-1 + -8x + 9x2) Add '-9x2' to each side of the equation. -9x + 9x2 + -9x2 = -1 + -8x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -9x + 0 = -1 + -8x + 9x2 + -9x2 -9x = -1 + -8x + 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -9x = -1 + -8x + 0 -9x = -1 + -8x Solving -9x = -1 + -8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8x' to each side of the equation. -9x + 8x = -1 + -8x + 8x Combine like terms: -9x + 8x = -1x -1x = -1 + -8x + 8x Combine like terms: -8x + 8x = 0 -1x = -1 + 0 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1
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