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Simplifying x2 + 10x + 21 = (x + 3)(x + 7) Reorder the terms: 21 + 10x + x2 = (x + 3)(x + 7) Reorder the terms: 21 + 10x + x2 = (3 + x)(x + 7) Reorder the terms: 21 + 10x + x2 = (3 + x)(7 + x) Multiply (3 + x) * (7 + x) 21 + 10x + x2 = (3(7 + x) + x(7 + x)) 21 + 10x + x2 = ((7 * 3 + x * 3) + x(7 + x)) 21 + 10x + x2 = ((21 + 3x) + x(7 + x)) 21 + 10x + x2 = (21 + 3x + (7 * x + x * x)) 21 + 10x + x2 = (21 + 3x + (7x + x2)) Combine like terms: 3x + 7x = 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 '-10x' to each side of the equation. 10x + -10x + x2 = 10x + -10x + x2 Combine like terms: 10x + -10x = 0 0 + x2 = 10x + -10x + x2 x2 = 10x + -10x + x2 Combine like terms: 10x + -10x = 0 x2 = 0 + x2 x2 = x2 Add '-1x2' to each side of the equation. x2 + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 0 Solving 0 = 0 Couldn't find a variable to solve for. This equation is an identity, all real numbers are solutions.
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