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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 = -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 = -6x 21 + -6x = -21 + -4x + 4x Combine like terms: -4x + 4x = 0 21 + -6x = -21 + 0 21 + -6x = -21 Add '-21' to each side of the equation. 21 + -21 + -6x = -21 + -21 Combine like terms: 21 + -21 = 0 0 + -6x = -21 + -21 -6x = -21 + -21 Combine like terms: -21 + -21 = -42 -6x = -42 Divide each side by '-6'. x = 7 Simplifying x = 7
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