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Simplifying (5d + -7)(5d + -6) = 25d2 + d + 62 Reorder the terms: (-7 + 5d)(5d + -6) = 25d2 + d + 62 Reorder the terms: (-7 + 5d)(-6 + 5d) = 25d2 + d + 62 Multiply (-7 + 5d) * (-6 + 5d) (-7(-6 + 5d) + 5d * (-6 + 5d)) = 25d2 + d + 62 ((-6 * -7 + 5d * -7) + 5d * (-6 + 5d)) = 25d2 + d + 62 ((42 + -35d) + 5d * (-6 + 5d)) = 25d2 + d + 62 (42 + -35d + (-6 * 5d + 5d * 5d)) = 25d2 + d + 62 (42 + -35d + (-30d + 25d2)) = 25d2 + d + 62 Combine like terms: -35d + -30d = -65d (42 + -65d + 25d2) = 25d2 + d + 62 Reorder the terms: 42 + -65d + 25d2 = 62 + d + 25d2 Add '-25d2' to each side of the equation. 42 + -65d + 25d2 + -25d2 = 62 + d + 25d2 + -25d2 Combine like terms: 25d2 + -25d2 = 0 42 + -65d + 0 = 62 + d + 25d2 + -25d2 42 + -65d = 62 + d + 25d2 + -25d2 Combine like terms: 25d2 + -25d2 = 0 42 + -65d = 62 + d + 0 42 + -65d = 62 + d Solving 42 + -65d = 62 + 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. 42 + -65d + -1d = 62 + d + -1d Combine like terms: -65d + -1d = -66d 42 + -66d = 62 + d + -1d Combine like terms: d + -1d = 0 42 + -66d = 62 + 0 42 + -66d = 62 Add '-42' to each side of the equation. 42 + -42 + -66d = 62 + -42 Combine like terms: 42 + -42 = 0 0 + -66d = 62 + -42 -66d = 62 + -42 Combine like terms: 62 + -42 = 20 -66d = 20 Divide each side by '-66'. d = -0.303030303 Simplifying d = -0.303030303
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