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Simplifying (x + -7)(x + -5) = x2 + -12x + d Reorder the terms: (-7 + x)(x + -5) = x2 + -12x + d Reorder the terms: (-7 + x)(-5 + x) = x2 + -12x + d Multiply (-7 + x) * (-5 + x) (-7(-5 + x) + x(-5 + x)) = x2 + -12x + d ((-5 * -7 + x * -7) + x(-5 + x)) = x2 + -12x + d ((35 + -7x) + x(-5 + x)) = x2 + -12x + d (35 + -7x + (-5 * x + x * x)) = x2 + -12x + d (35 + -7x + (-5x + x2)) = x2 + -12x + d Combine like terms: -7x + -5x = -12x (35 + -12x + x2) = x2 + -12x + d Reorder the terms: 35 + -12x + x2 = d + -12x + x2 Add '12x' to each side of the equation. 35 + -12x + 12x + x2 = d + -12x + 12x + x2 Combine like terms: -12x + 12x = 0 35 + 0 + x2 = d + -12x + 12x + x2 35 + x2 = d + -12x + 12x + x2 Combine like terms: -12x + 12x = 0 35 + x2 = d + 0 + x2 35 + x2 = d + x2 Add '-1x2' to each side of the equation. 35 + x2 + -1x2 = d + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + 0 = d + x2 + -1x2 35 = d + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 = d + 0 35 = d Solving 35 = d Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-1d' to each side of the equation. 35 + -1d = d + -1d Combine like terms: d + -1d = 0 35 + -1d = 0 Add '-35' to each side of the equation. 35 + -35 + -1d = 0 + -35 Combine like terms: 35 + -35 = 0 0 + -1d = 0 + -35 -1d = 0 + -35 Combine like terms: 0 + -35 = -35 -1d = -35 Divide each side by '-1'. d = 35 Simplifying d = 35
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