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Simplifying (x2) + -10x + 21 = (x + -3)(x + 7) 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 = 4x 21 + -10x + x2 = (-21 + 4x + x2) Add '-1x2' to each side of the equation. 21 + -10x + x2 + -1x2 = -21 + 4x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -10x + 0 = -21 + 4x + x2 + -1x2 21 + -10x = -21 + 4x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 21 + -10x = -21 + 4x + 0 21 + -10x = -21 + 4x Solving 21 + -10x = -21 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 21 + -10x + -4x = -21 + 4x + -4x Combine like terms: -10x + -4x = -14x 21 + -14x = -21 + 4x + -4x Combine like terms: 4x + -4x = 0 21 + -14x = -21 + 0 21 + -14x = -21 Add '-21' to each side of the equation. 21 + -21 + -14x = -21 + -21 Combine like terms: 21 + -21 = 0 0 + -14x = -21 + -21 -14x = -21 + -21 Combine like terms: -21 + -21 = -42 -14x = -42 Divide each side by '-14'. x = 3 Simplifying x = 3
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