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Simplifying x2 + -10x + 21 = (x + 7)(x + 3) Reorder the terms: 21 + -10x + x2 = (x + 7)(x + 3) Reorder the terms: 21 + -10x + x2 = (7 + x)(x + 3) Reorder the terms: 21 + -10x + x2 = (7 + x)(3 + x) Multiply (7 + x) * (3 + x) 21 + -10x + x2 = (7(3 + x) + x(3 + x)) 21 + -10x + x2 = ((3 * 7 + x * 7) + x(3 + x)) 21 + -10x + x2 = ((21 + 7x) + x(3 + x)) 21 + -10x + x2 = (21 + 7x + (3 * x + x * x)) 21 + -10x + x2 = (21 + 7x + (3x + x2)) Combine like terms: 7x + 3x = 10x 21 + -10x + x2 = (21 + 10x + x2) Add '-21' to each side of the equation. 21 + -10x + -21 + x2 = 21 + 10x + -21 + x2 Reorder the terms: 21 + -21 + -10x + x2 = 21 + 10x + -21 + x2 Combine like terms: 21 + -21 = 0 0 + -10x + x2 = 21 + 10x + -21 + x2 -10x + x2 = 21 + 10x + -21 + x2 Reorder the terms: -10x + x2 = 21 + -21 + 10x + x2 Combine like terms: 21 + -21 = 0 -10x + x2 = 0 + 10x + x2 -10x + x2 = 10x + x2 Add '-1x2' to each side of the equation. -10x + x2 + -1x2 = 10x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10x + 0 = 10x + x2 + -1x2 -10x = 10x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10x = 10x + 0 -10x = 10x Solving -10x = 10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. -10x + -10x = 10x + -10x Combine like terms: -10x + -10x = -20x -20x = 10x + -10x Combine like terms: 10x + -10x = 0 -20x = 0 Divide each side by '-20'. x = 0 Simplifying x = 0
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